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{"segments": [{"id": 1, "seek": 3054, "start": 1.58, "end": 30.54, "text": "ุจุณู
ุงููู ุงูุฑุญู
ู ุงูุฑุญูู
ุฃุนุฒุงุก ุงูุทูุงุจ ุงูุณูุงู
ุนูููู
ูุฑุญู
ุฉ ุงููู ูุจุฑูุงุชู ูู ูุฐุง ุงูููุฏูู ุณูุดูุฑ ุงู ุดุงุก ุงููู ุชุทุจูู ุงูุชุงูู ููุชูุงู
ู ุงูู
ุญุฏูุฏ ูู section 6 3 ุจุนููุงู arc length ุณูุนุฑู ููู ูุญุณุจ ุทูู ุงูู
ูุญูุฉ ุจุงุณุชุฎุฏุงู
ุงูุชูุงู
ู ุงูู
ุญุฏูุฏ ูู ุฃูุง ุนูุฏู .. ูู
ุง ุชุดูููู ูู ุงูุดูู ูุฐุง ุฏุงูุฉ ุจููู ุฃุฒุฑู ูุจูุนุฑู ูุฏู ุทูู ุงูู
ูุญูุฉ ูุฐุง ุงููู ูู ุจููู ุฃุฒุฑู ุนูู ุงููุชุฑุฉ X ู
ู A ูB", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 5551, 3615, 11622, 16606, 41950, 15040, 3555, 21136, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224, 8978, 23758, 27188, 1829, 16254, 2407, 8608, 1863, 8592, 3224, 2288, 16472, 13412, 16606, 21984, 6055, 9566, 21292, 4587, 16712, 7649, 1829, 24976, 2655, 4117, 10943, 1211, 9673, 24401, 23328, 31439, 3541, 1386, 805, 45030, 1863, 2407, 7649, 10346, 4641, 8608, 1863, 3615, 28480, 9122, 33911, 8717, 5016, 35457, 23032, 12610, 9673, 1211, 5016, 1863, 3660, 4724, 995, 14851, 9778, 3215, 10943, 16712, 4117, 10943, 1211, 9673, 24401, 23328, 45164, 41850, 43242, 4117, 4386, 9122, 15042, 6055, 8592, 38688, 11536, 8978, 25124, 28820, 23758, 11778, 6027, 3660, 4724, 1211, 11536, 5551, 11622, 2288, 4587, 6156, 3555, 1863, 3615, 28480, 9122, 3215, 3224, 23032, 12610, 9673, 1211, 5016, 1863, 3660, 23758, 13672, 1829, 31439, 4724, 1211, 11536, 5551, 11622, 2288, 4587, 15844, 27188, 2655, 25720, 1783, 9154, 316, 5296, 33], "avg_logprob": -0.21132812043651938, "compression_ratio": 1.9335548172757475, "no_speech_prob": 7.152557373046875e-07, "words": [{"start": 1.58, "end": 1.88, "word": "ุจุณู
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ู", "probability": 0.962890625}, {"start": 2.5, "end": 2.92, "word": " ุงูุฑุญูู
", "probability": 0.9930013020833334}, {"start": 2.92, "end": 3.28, "word": " ุฃุนุฒุงุก", "probability": 0.69122314453125}, {"start": 3.28, "end": 3.62, "word": " ุงูุทูุงุจ", "probability": 0.93505859375}, {"start": 3.62, "end": 3.9, "word": " ุงูุณูุงู
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", "probability": 0.960693359375}, {"start": 4.24, "end": 4.52, "word": " ูุฑุญู
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ุง", "probability": 0.826904296875}, {"start": 20.88, "end": 21.28, "word": " ุชุดูููู", "probability": 0.6905517578125}, {"start": 21.28, "end": 21.38, "word": " ูู", "probability": 0.7578125}, {"start": 21.38, "end": 21.8, "word": " ุงูุดูู", "probability": 0.976318359375}, {"start": 21.8, "end": 22.1, "word": " ูุฐุง", "probability": 0.74560546875}, {"start": 22.1, "end": 22.96, "word": " ุฏุงูุฉ", "probability": 0.6695149739583334}, {"start": 22.96, "end": 23.42, "word": " ุจููู", "probability": 0.7240397135416666}, {"start": 23.42, "end": 23.92, "word": " ุฃุฒุฑู", "probability": 0.8458251953125}, {"start": 23.92, "end": 25.42, "word": " ูุจูุนุฑู", "probability": 0.8369140625}, {"start": 25.42, "end": 25.64, "word": " ูุฏู", "probability": 0.7571614583333334}, {"start": 25.64, "end": 25.94, "word": " ุทูู", "probability": 0.905029296875}, {"start": 25.94, "end": 26.46, "word": " ุงูู
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ูุฌูุฏ ูุฏุงู
ูุง Definition if f' is continuous on the closed interval a ูb ุงูู ุดุฑุท ุงู ุชููู ุงูุฏุงูุฉ ูุจู ุงูุงุดุชุบุงู ูู
ุณุชูููุง ู
ุชุตูุฉ ุนูู ุงููุชุฑุฉ ู
ู a ุงูู b Then the length ุทูู ุงูุงุฑู ุทูู ุงูู
ูุญูุฉ ุนููุง of the curve y ุจูุณุงูู f of x from point a", "tokens": [6027, 2655, 3615, 16572, 5172, 3714, 29245, 23328, 12174, 3215, 10943, 8315, 46245, 849, 498, 283, 6, 307, 10957, 322, 264, 5395, 15035, 257, 4032, 65, 1975, 12610, 13412, 2288, 9566, 16472, 6055, 30544, 32748, 6027, 3660, 12174, 36150, 2423, 33599, 2655, 17082, 6027, 4032, 2304, 14851, 4587, 1211, 11296, 44650, 36520, 3660, 15844, 27188, 2655, 25720, 9154, 257, 2423, 7578, 272, 1396, 264, 4641, 23032, 12610, 2423, 9640, 4117, 23032, 12610, 9673, 1211, 5016, 1863, 3660, 11203, 8315, 295, 264, 7605, 288, 4724, 1829, 3794, 995, 45865, 283, 295, 2031, 490, 935, 257], "avg_logprob": -0.4177631560124849, "compression_ratio": 1.446808510638298, "no_speech_prob": 0.0, "words": [{"start": 33.089999999999996, "end": 33.77, "word": "ุงูุชุนุฑูู", "probability": 0.88408203125}, {"start": 33.77, "end": 34.33, "word": " ู
ูุฌูุฏ", "probability": 0.75634765625}, {"start": 34.33, "end": 34.91, "word": " ูุฏุงู
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ุดุชูุฉ", "tokens": [10721, 12610, 11331, 26108, 3660, 8717, 7435, 1829, 3555, 11296, 9673, 8592, 2655, 28671], "avg_logprob": -0.5291666507720947, "compression_ratio": 0.86, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 78.58999999999999, "end": 79.99, "word": "ุฃูู", "probability": 0.246673583984375}, {"start": 79.99, "end": 81.39, "word": " ุญุงุฌุฉ", "probability": 0.7322591145833334}, {"start": 81.39, "end": 83.41, "word": " ูุฌูุจูุง", "probability": 0.70576171875}, {"start": 83.41, "end": 84.59, "word": " ุงูู
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ุน ุงููุงุญุฏ ู ุจุนุฏูู ูุนู
ู ุงุฎุชุตุงุฑุงุช ู ุงุฐุง ูุงู ู
ูุฌูุฏ ููุงุฎุฏ ุฌุฐุฑ ุงูุชุฑุจูุนู ุฎุจุฑุฉ ูุงู
ู ุนุฑููุง ู
ู A ู B ููุงุฎุฏ ุงูู ู
ุซุงู example find the length of the curve Y ุจูุณูุก 4 ูู ุฌุฐุฑ 2 ุนูู 3 X ุงู 3 ุน 2 ููุต 1 ู X ู
ู 0 ู 1 ูุงู ุงู Y ุนูุฏูุง ุจูุฌูุจ ุงูู
ุดุชูุฉ ุงูุฃููู ุงูู
ุดุชูุฉ ุงูุฃููู ุงููู ูู Y run dy dx ุจูุณูุก 2 ุฌุฐุฑ 2 ูู X ูุตู ู ุชูุงุญุธูุง ุงููุง ู
ุชุตู ุน ุงููุชุฑุฉ ู
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ู ู
ู ุตูุฑ ุงููุงุญุฏ ูุฌุฏุฑ ูุงุญุฏ ุฒู ุงูู
ุฑุจุน ุงูู
ุดุชูู ูุณุงูู ุงูุชูุงู
ู ู
ู ุตูุฑ ุงููุงุญุฏ ูุฌุฏุฑ ูุงุญุฏ ุฒู 8x dx ููู ุจูุตูุฑ ุณุคุงู ุชูุงู
ู ุนูู ุงููุงุนุฏุฉ ุจุงุณุชุฎุฏุงู
ุงูุชุนููุถ ุฒู ู
ุง ุชูุชูุง ูู ุดุจุท ุงูุฎู
ุณุฉ ูุฎู ุงู U ุชุณุงูู 1 ุฒู 8x ูุจูุตูุฑ ุนูุฏ ุงู D U ุนุจุงุฑุฉ ุนู 8DX ูู ุจูุตูุฑ ุงูุชูุงู
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ุงููุฉ ูู ูุงุญุฏ ุฒู ุชู
ุงููุฉ X ุงุฒ ุชูุชุฉ ุน ุงุชููู ูุงู X ู
ุถุงูู ู
ู ูุงุญุฏ ูุฒูุฑู ูู
ุซุงู ุชุงูู find the length of the graph of X ุงุฒ ุชูุชุฉ ุน ุงุชููู ุฒู ุชู
ุงููุฉ X ุงุฒ ุชูุชุฉ ุน ุงุชููู ู X ู
ู ูุงุญุฏ ูุงุฑุจุน ูุฌูุจ ุงูู
ุดุชูุฉ ุงูุงููู X ุชุฑุจูุน ุนูู ุงุฑุจุน ููุต ูุงุญุฏ ุนูู X ุชุฑุจูุน ููู ุนูู ุงููุชุฑุฉ ุงููู ุนูุฏูุง ู
ุชุตูุฉ ูุฑุจููุง ููุถูู ุงูู ูุงุญุฏ ููุนู
ู ุชุจุณูุท", "tokens": [2655, 1211, 2655, 9957, 8978, 36764, 24401, 3660, 46811, 7649, 10632, 8978, 36764, 24401, 30767, 1829, 46811, 7649, 10632, 1783, 1975, 11622, 6055, 1211, 2655, 3660, 6225, 1975, 2655, 1863, 9957, 16070, 1783, 3714, 11242, 47302, 4587, 9154, 36764, 24401, 5296, 11622, 1829, 32887, 4032, 2304, 12984, 6027, 6055, 7649, 1829, 915, 264, 4641, 295, 264, 4295, 295, 1783, 1975, 11622, 6055, 1211, 2655, 3660, 6225, 1975, 2655, 1863, 9957, 30767, 1829, 46811, 7649, 10632, 1783, 1975, 11622, 6055, 1211, 2655, 3660, 6225, 1975, 2655, 1863, 9957, 4032, 1783, 9154, 36764, 24401, 5296, 9640, 3555, 3615, 8717, 7435, 1829, 3555, 9673, 8592, 2655, 28671, 42963, 12610, 7578, 1783, 6055, 2288, 21292, 3615, 15844, 1975, 25513, 3615, 8717, 4587, 9381, 36764, 24401, 15844, 1783, 6055, 2288, 21292, 3615, 37037, 1829, 15844, 27188, 2655, 25720, 13672, 1829, 43242, 8315, 44650, 36520, 3660, 8717, 2288, 21292, 11296, 4032, 1863, 11242, 33911, 2423, 7578, 36764, 24401, 4032, 1863, 25957, 1211, 6055, 3555, 3794, 1829, 9566], "avg_logprob": -0.358989182813668, "compression_ratio": 2.2278481012658227, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 142.02, "end": 142.56, "word": "ุชูุชูู", "probability": 0.6792449951171875}, {"start": 142.56, "end": 143.1, "word": " ูู", "probability": 0.56103515625}, {"start": 143.1, "end": 143.54, "word": " ูุงุญุฏุฉ", "probability": 0.84521484375}, {"start": 143.54, "end": 143.9, "word": " ุชู
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ุงููุฉ", "probability": 0.7375081380208334}, {"start": 144.86, "end": 145.04, "word": " X", "probability": 0.55810546875}, {"start": 145.04, "end": 145.2, "word": " ุงุฒ", "probability": 0.23046875}, {"start": 145.2, "end": 145.44, "word": " ุชูุชุฉ", "probability": 0.7928466796875}, {"start": 145.44, "end": 145.52, "word": " ุน", "probability": 0.64990234375}, {"start": 145.52, "end": 145.86, "word": " ุงุชููู", "probability": 0.8253173828125}, {"start": 145.86, "end": 146.04, "word": " ูุงู", "probability": 0.366455078125}, {"start": 146.04, "end": 146.18, "word": " X", "probability": 0.483154296875}, {"start": 146.18, "end": 146.44, "word": " ู
ุถุงูู", "probability": 0.52471923828125}, {"start": 146.44, "end": 146.56, "word": " ู
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ุนูุงู ุงูู
ูุฏุงุฑ X ุชุฑุจูุน ุนูู ุฃุฑุจุน ุฒู ูุงุญุฏ ุนูู X ุชุฑุจูุน ููู ุชุฑุจูุน ูุฐุง ู
ุง ูุถููู ุงููุงุญุฏ ูุฐุง ู
ุง ูุถููู ูุตู ูุฐุง ู
ุง ูุถููู ู
ุฑุจุน ูุงู
ู ูู ุจุงูุตูุฑุฉ ูุฐู ุงุฐุง ูุงู ุชุณุงูู ุงูุชูุงู
ู ู
ู ูุงุญุฏ ูุฃุฑุจุน ุนูู ุฌุฏุฑ ูุงุญุฏ ุฒู ุฃูุจุฑ ุจุฑุงู
ู X ููู ุชุฑุจูุน DX ูุฐุง ุงููุงุนุฏุฉ ุชุณุงูู ุงูุชูุงู
ู ู
ู ูุงุญุฏ ูุฃุฑุจุน ูุฐุง ู
ุง ุญุณุจูุงู ูู X ุชุฑุจูุน ุนูู ุฃุฑุจุน ุฒู ูุงุญุฏ ุนูู X ุชุฑุจูุน ููู ุชุฑุจูุน", "tokens": [2655, 19913, 3224, 2288, 20449, 8315, 3224, 9673, 28543, 9640, 1783, 6055, 2288, 21292, 3615, 15844, 5551, 25513, 3615, 30767, 1829, 36764, 24401, 15844, 1783, 6055, 2288, 21292, 3615, 5296, 28820, 6055, 2288, 21292, 3615, 23758, 19446, 8717, 11242, 1829, 4587, 3224, 2423, 14407, 24401, 23758, 19446, 8717, 11242, 1829, 4587, 3224, 8717, 9381, 5172, 23758, 19446, 8717, 11242, 1829, 4587, 3224, 3714, 25513, 3615, 9122, 10943, 1211, 39896, 20666, 9381, 13063, 3660, 29538, 1975, 15730, 50239, 6055, 3794, 995, 45865, 16712, 4117, 10943, 1211, 9154, 36764, 24401, 5296, 10721, 25513, 3615, 15844, 10874, 3215, 2288, 36764, 24401, 30767, 1829, 5551, 4117, 26890, 4724, 2288, 10943, 1829, 1783, 5296, 28820, 6055, 2288, 21292, 3615, 48817, 23758, 25062, 995, 22488, 3660, 6055, 3794, 995, 45865, 16712, 4117, 10943, 1211, 9154, 36764, 24401, 5296, 10721, 25513, 3615, 23758, 19446, 11331, 35457, 8315, 3224, 31439, 1783, 6055, 2288, 21292, 3615, 15844, 5551, 25513, 3615, 30767, 1829, 36764, 24401, 15844, 1783, 6055, 2288, 21292, 3615, 5296, 28820, 6055, 2288, 21292, 3615], "avg_logprob": -0.32663689748871894, "compression_ratio": 2.748792270531401, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 168.46, "end": 169.06, "word": "ุชุธูุฑ", "probability": 0.64794921875}, {"start": 169.06, "end": 169.6, "word": " ู
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ููุง ุชูู
ููุง x ุงุด ุชูุงุชุฉ ุนูู ุงุชูุงุด ูุฎุณ ูุงุญุฏ ุนูู x ู ุงู x ุจูุบูุฑ ู
ู ูุงุญุฏ ูุงุฑุจุน ุจูุนู
ู ุจุงูุญุฏูุฏ ุงูุงุฑุจุน ุจุนุฏูู ุงููุงุญุฏ ุฏูููู ุงููู ูู ุงุชููู ู ุณุจุนูู ุนูู ุงุชูุงุด ุงููู ุจูุณุงูู ุณุชุฉ ุงุฐุง ุทูู ุณุช ูุงุญุฏุงุช ููุณ ุงูุงุดู ุจุณ ุงูุชูุงู
ู ูู
ุง ุชููู ุจุงููุณุจุฉ ูู y ูู ูุงูุช ุงู x ุงู function y ุชุณุงูู g of y ู y ุจูุบูุฑ ู
ู c ู d ููู ุฌู ุจุฑุงู ู
ุชุตู ุนูู ุงููุทุฑ ู
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ูุญุงูุฉ X ุงูู
ุฏูุฉ ูู ุงูู Y ูุณุงูู ุงูุชูุงุจ ู
ู C ูD ูุฌุฏุฑ 1 ุฒุงุฆุฏ ู
ุดุชูุฉ X ู
ู ุณูุฑ Y ูู ุชุบููุฑ D Y ูุงุฎุฏ ุนููู ุงูู
ุซุงู ูู ู
ุฏููุฉ F ุนูุฏูุง length of the curve Y ุจุณุงูู X ุนูู 2 ู
ุณุชุซููู from X ุชุณุงูู ุณูุฑ 2 ูุนุธู
ุนุงูู
ู
ุฏููุฉ Y ู
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ู ุตูุฑ ุฅูู ุงุชููู ูู ุฃุฎุฏูุง ุงูู
ุดุชูุฉ ุงูุฃููู ุงูู
ุดุชูุฉ ุงูุฃููู ุชุณุงูู ุชูุช ูู ุงุชููู ุนูู ุงูุณ ุชูุช ูู ุฃุฎุฏูุง ุงููุชุฑุฉ ูุฐู ุงูุฏููุฉ ุบูุฑ ู
ุชุตูุฉ ุนูู ุงููุชุฑุฉ ูููุง ูุฃู ุนูุฏ ุงูุณูุฑ ุบูุฑ ู
ุชุตูุฉ ูุฃู ุบูุฑ ู
ุชุตูุฉ ุนูู ุงููุชุฑุฉ ู
ู ุตูุฑ ุงููุงุญุฏ ุฅูู ุงุชููู ูุงุญุฏ ู
ู ุงูุดุฑูุท ูุงุฒู
ุชููู ุงู ุงูู
ุดุชูุฉ ุงูุฃููู ู
ุชุตูุฉ ุนูู ุงููุชุฑุฉ ุงูู
ุงุถูุฉ ุงุฐุง ุงูุง ู
ุงูุฏุฑุด ุงูู
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ุน ุจุนุถ ุงู x ุนูู ุงุชููู ููุฐุง ุจูุตูุฑ y ุชูุช ุนูู ุงุชููู ูุงุฎุฏ ุงู x ูุญุงูุฉ ูุทุงูุจ ูุถุฑุจ ูู ุงุชููู ูุจุตูุฑ ุงู x ูุณุงูู ุงุชููู ูู y ุชูุช ุนูู ุงุชููู ููู ุทูุนูุง ุงู x ู function ูู ุงู y ุจุงููุณุจุฉ ููุญุฏูุฏ ุงูุชูุงู
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ุง ุงู X ุชุณูู ุงุชููู ูุถุน ุงุชููู ุจุฏููู ูุงุญุฏ ุงู Y ูุชุบูุฑ ู
ู ุณูุฑ ููุงุญุฏ ูุฌูุจ ุงูู
ุดุชูุฉ ุชุจูู X ุจุงููุณุจุฉ ู Y ุงูู
ุดุชูุฉ ุชุณูู ุชูุงุชุฉ ูู Y ุงุต ูุต ุงู Y ู
ู ุงูุณูุฑ ููุงุญุฏ ู
ุชุตู ุนูู ุงููุชุฑุฉ ู
ู ุงูุณูุฑ ููุงุญุฏ ุงููุชุฑุฉ ู
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ุซููุง ุฏู ุฌุฏุฑ ูุงุญุฏ ุฒู ุงูู
ุดุชูุฉ ุงูุฃููู ูู x ุจุงููุณุจุงูู ููุณุงูู ุชูุงู
ู ู
ู ุตูุฑ ููุงุญุฏ ุฒู ุฌุฏุฑ ูุงุญุฏ ุฒู ุงูุชุณุนุฉ y dy ูููุณ ุงูุดูุก ูุงุฎุฏ ุงู U ุชุณุงูู ูุงุญุฏ ุฒู ุงูุชุณุนุฉ y ูุนูุฏูุง ุงูุจุฑุงู
ุฌ ุงููุงู
ูุฉ ููุง ุฏู ุชุณุงูู ูุงุญุฏ ุฒู ุงูุชุณุนุฉ y ุงู ุชูุชุฉ ุนูู ุงุชููู ู
ูุณูู
ุนูู ุชูุชุฉ ุนูู ุงุชููู ูุนูู ู
ุถู
ูู ูู ุชูุชูู ูุงูุชุณุนุฉ ูู ุฌุงู
ุน ู
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ูุฉ ุฏุฑุณูุงูุง ูู ุงูู Classic Chapter 5 ุฒู ูู ููุง ูุนู
ู ุฃุณุฆูุฉ ูุซูุฑุฉ ุญุฌูุฒ ุชูุงู
ู ุงูุง ุนูุฏู ุงู world ุบูุฑ ู
ู ุตูุฑ ููุงุญุฏ ู ุจูุนูุฏ ุจุงูุญุฏูุฏ ู ุจุทูุน ูุฐุง ุงูู
ูุฏุงุฑ ู
ุนูุงู ุงููู ูู ุทูู ุงูู
ูุญุงูุฉ ูู ุงููุง ูุบุฉ ุชูุทุฉ ูุงุญุฏุฉ ุงููู ูู differential formula of world arc length ุงูู ุงุญูุง ูุงู ุฏุงุฆู
ุง ูุทูุน ู
ู ุฌูุง ุจุนุฏุฏ ูุฃู ุงูุง ุนูุฏู ุญุฌูุฒ ุชูุงู
ู ู
ูุฌูุฏุฉ ู
ู ุตูุฑ ููุงุญุฏ ููู ุงุฎุฏูุง ููุง ูุงูุช ุงูููุทุฉ ู
ุด ู
ูุฌูุฏุฉ ู
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ุฑุญูุฉ ู
ุชุบูุฑ ูู ุฎุฏูุง ุงู arc length function s of x ูู ุงูุชูุงู
ู ู
ู a ูx ูุงู arc length function s of x ูู ุงูุชูุงู
ู ู
ู 1 ูx ุฌุฏุฑ ูุงุญุฏ ุฒู ุงู arc length", "tokens": [3224, 1829, 9566, 1211, 3615, 25724, 14407, 3555, 16472, 23032, 12610, 3714, 2288, 5016, 37977, 3714, 2655, 17082, 13546, 45164, 16490, 3215, 8315, 2423, 10346, 4641, 2445, 262, 295, 2031, 39896, 16712, 4117, 10943, 1863, 9154, 257, 5296, 87, 6156, 6027, 10346, 4641, 2445, 262, 295, 2031, 39896, 16712, 4117, 10943, 1863, 9154, 502, 5296, 87, 10874, 3215, 2288, 36764, 24401, 30767, 1829, 2423, 10346, 4641], "avg_logprob": -0.4771455223880597, "compression_ratio": 1.6619718309859155, "no_speech_prob": 0.0, "words": [{"start": 379.37, "end": 379.71, "word": "ููุทูุน", "probability": 0.6095703125}, {"start": 379.71, "end": 380.13, "word": " ุงูุฌูุงุจ", "probability": 0.9415690104166666}, {"start": 380.13, "end": 380.35, "word": " ุงู", "probability": 0.340087890625}, {"start": 380.35, "end": 381.13, "word": " ุทูู", "probability": 0.77978515625}, {"start": 381.13, "end": 381.45, "word": " ู
ุฑุญูุฉ", "probability": 0.7576904296875}, {"start": 381.45, "end": 382.45, "word": " ู
ุชุบูุฑ", "probability": 0.812255859375}, {"start": 382.45, "end": 383.81, "word": " ูู", "probability": 0.44921875}, {"start": 383.81, "end": 384.07, "word": " ุฎุฏูุง", "probability": 0.694091796875}, {"start": 384.07, "end": 390.59, "word": " ุงู", "probability": 0.368408203125}, {"start": 390.59, "end": 391.51, "word": " arc", "probability": 0.41357421875}, {"start": 391.51, "end": 392.09, "word": " length", "probability": 0.73486328125}, {"start": 392.09, "end": 392.67, "word": " function", "probability": 0.8408203125}, {"start": 392.67, "end": 392.93, "word": " s", "probability": 0.2342529296875}, {"start": 392.93, "end": 393.09, "word": " of", "probability": 0.1580810546875}, {"start": 393.09, "end": 393.39, "word": " x", "probability": 0.86279296875}, {"start": 393.39, "end": 393.61, "word": " ูู", "probability": 0.77587890625}, {"start": 393.61, "end": 394.19, "word": " ุงูุชูุงู
ู", "probability": 0.818603515625}, {"start": 394.19, "end": 394.39, "word": " ู
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ู", "probability": 0.950439453125}, {"start": 400.05, "end": 400.17, "word": " ู
ู", "probability": 0.9150390625}, {"start": 400.17, "end": 400.27, "word": " 1", "probability": 0.57177734375}, {"start": 400.27, "end": 400.61, "word": " ูx", "probability": 0.787841796875}, {"start": 400.61, "end": 400.95, "word": " ุฌุฏุฑ", "probability": 0.6162007649739584}, {"start": 400.95, "end": 401.11, "word": " ูุงุญุฏ", "probability": 0.864990234375}, {"start": 401.11, "end": 401.29, "word": " ุฒู", "probability": 0.556884765625}, {"start": 401.29, "end": 401.43, "word": " ุงู", "probability": 0.50439453125}, {"start": 401.43, "end": 401.51, "word": " arc", "probability": 0.36181640625}, {"start": 401.51, "end": 401.87, "word": " length", "probability": 0.5517578125}], "temperature": 1.0}, {"id": 16, "seek": 42827, "start": 407.51, "end": 428.27, "text": "ูุงุฎุฏ ุนูู ุงูู
ุซุงู find the arc length function ุงุฐุง ููุช ุจุชุทูุจ arc length function for the curve in example two taking a ุจุฏูู ู
ู a ููุทุฉ ูุงุญุฏ ูุตููุฉ ุงููุงุญุฏ ุชูุงุชุงุดุฑ ุงุชูุงุดุฑ ุงุชูุงุดุฑ ูุงุฎุฏ ูุฐู ุงูููุทุฉ ูุญุธุฉ ุงูุฃุณูู ูุณุญุจ ุชูุงู
ู ูุงุญุฏ ุงูุงูุชุฑุงุฌุงุช ุงููุงุญุฏุฉ ุงุฒุงุฏ ุงูุชุฑุงุฌุงุช ุงูุชุฑุงุฌุงุช ุงูุชุฑุงุฌุงุช", "tokens": [1863, 47283, 3215, 15844, 9673, 12984, 6027, 915, 264, 10346, 4641, 2445, 1975, 15730, 9122, 29399, 39894, 9566, 46152, 10346, 4641, 2445, 337, 264, 7605, 294, 1365, 732, 1940, 257, 47525, 9957, 9154, 257, 8717, 47432, 3660, 36764, 24401, 4032, 9381, 12610, 3660, 2423, 14407, 24401, 6055, 1211, 9307, 33599, 2288, 1975, 2655, 1863, 33599, 2288, 1975, 2655, 1863, 33599, 2288, 8717, 47283, 3215, 29538, 28239, 47432, 3660, 5296, 5016, 19913, 3660, 16247, 3794, 5172, 1211, 7251, 3794, 5016, 3555, 6055, 4117, 10943, 1211, 36764, 24401, 42963, 4117, 2655, 2288, 26108, 9307, 2423, 14407, 24401, 3660, 1975, 11622, 18513, 1975, 4117, 2655, 2288, 26108, 9307, 1975, 4117, 2655, 2288, 26108, 9307, 1975, 4117, 2655, 2288, 26108, 9307], "avg_logprob": -0.5354872820741039, "compression_ratio": 1.8201754385964912, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 407.51, "end": 408.05, "word": "ูุงุฎุฏ", "probability": 0.5076904296875}, {"start": 408.05, "end": 408.19, "word": " ุนูู", "probability": 0.29736328125}, {"start": 408.19, "end": 408.75, "word": " ุงูู
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T ุชุฑุจู ุนูู 4 ุฒู 1 ุนูู T ุชุฑุจูู ุทุจุนุง ุงุณุชุจุฏููุง ููุง ุงููู ูู ุงู X ุงุณุชุจุฏููุง ููุง ุจุงู T ูุฃู ุงูุญุฏูุฏ ุงูุชูุงู
ู ูููุง X ุจูุงูุนุด ุงููู ููุง X ูููุง X ูุจุงููุงู
ู ูุจุทูุน ูุจุนุฏูู ุจูุนู
ู ุจุงูุญุฏูุฏ ุงู ุชูุงู
ู ุจุงูุญุฏูุฏ ูุฐู ุงูู
ูุนูุถุฉ ุนู T ุจ X ุจุฏููู X ุชูุงู
ู ุนูู 12 ููุต ูุงุญุฏุฉ X ููุต ุงูู
ูุนูุถ ุจุงููุงุญุฏ ุจุฏููู ุงููู ูู ููุต 11 ุนูู 12 ุจูุญุณุจูู
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ุฉ ูู X ุจุนุฏ ุงููุงุญุฏ ูุนูู ุฒู ุงุชููู ุงู ุชูุงุชุฉ ุจููุฏุฑ ูุฌูุจ ุงูุงุณู
ุงููู ูู ู
ุซูุง ุนูุฏูุง ููุทุฉ ุทูุจูุง ู
ุซูุง ุงูููุทุฉ ุงููู ุจุฏูุง ูููุง ุงูู E1 ู E3 ู E12 ุฅูู ุงูููุทุฉ ุจูู E4 ู 67 ุนูู 12 ุซู
ุงุญูุง ุจุงูู
ูุง ุงู X ููุง ูุงุญุฏ ู ููุง X ุฃุฑุจุน ูุงุณ ุงูุงุฑุจุน ููุฌูุจ ููุง", "tokens": [1211, 2407, 1975, 3615, 9566, 1829, 8315, 1975, 1829, 12174, 32640, 3660, 5296, 39184, 1783, 39182, 2423, 14407, 24401, 37495, 22653, 30767, 1829, 1975, 2655, 1863, 9957, 1975, 2407, 6055, 1211, 9307, 3660, 4724, 1829, 28543, 2288, 8717, 7435, 1829, 3555, 2423, 32277, 2304, 13672, 1829, 31439, 50113, 15040, 43242, 8315, 8717, 47432, 3660, 23032, 46152, 8315, 50113, 15040, 28239, 47432, 3660, 13672, 1829, 47525, 8315, 8978, 11296, 2423, 39184, 462, 16, 4032, 462, 18, 4032, 462, 4762, 30731, 28239, 47432, 3660, 4724, 1829, 3224, 462, 19, 4032, 23879, 15844, 2272, 38637, 2304, 1975, 5016, 8315, 4724, 995, 16095, 8315, 2423, 1783, 34105, 36764, 24401, 4032, 34105, 1783, 5551, 25513, 3615, 6156, 32277, 2423, 9640, 3555, 3615, 8032, 1863, 7435, 1829, 3555, 34105], "avg_logprob": -0.43901209196736735, "compression_ratio": 1.9027777777777777, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 468.55, "end": 468.93, "word": "ูู", "probability": 0.48345947265625}, {"start": 468.93, "end": 469.61, "word": " ุงุนุทููุง", "probability": 0.7990234375}, {"start": 469.61, "end": 469.79, "word": " ุงู", "probability": 0.6680908203125}, {"start": 469.79, "end": 470.25, "word": " ููู
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ู ุณูููู ู
ู ูุงุญุฏ ุฅูู ุฃุฑุจุนุฉ ูุฃุณุณ ุงูุฃุฑุจุนุฉ ู
ู ุนูุถ ุณูุจูู ุฃุฑุจุนุฉ ุจุฏู X ุจุฏู ููู ูู ุณุชุฉ ููู ููุณ ุงูุฌูุงุจ ุงููู ุฃุฎุฏูุงู ูู ุงูู
ุซุงู ุงุชููู ุณูุฎุชุงุฑ ุงูุฃู
ุซูุฉ Find the length of the curves in exercises ู
ู ูุงุญุฏ ุฅูู ุนุดุฑุฉ ุงุฐุง ููุง ูุฌูุจ ุฃุทูู ุงูู
ูุญูุงุช ูุฃุณุงุณ ู
ู ูุงุญุฏ ุฅูู ุนุดุฑุฉ ุณุฃุฎุฏ ุณุคุงู ุชุณุนุฉ X ุณูู ุงูุชูุงู
ู ู
ู ุณุคุงู Y ูุฃุฌูุฒุฉ 6 4T-1DT ูY ู
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ู", "probability": 0.92431640625}, {"start": 510.13, "end": 510.25, "word": " ูุงุญุฏ", "probability": 0.985107421875}, {"start": 510.25, "end": 510.33, "word": " ุฅูู", "probability": 0.80615234375}, {"start": 510.33, "end": 510.53, "word": " ุนุดุฑุฉ", "probability": 0.8899739583333334}, {"start": 510.53, "end": 510.73, "word": " ุณุฃุฎุฏ", "probability": 0.55291748046875}, {"start": 510.73, "end": 510.97, "word": " ุณุคุงู", "probability": 0.8880208333333334}, {"start": 510.97, "end": 511.95, "word": " ุชุณุนุฉ", "probability": 0.81689453125}, {"start": 511.95, "end": 512.23, "word": " X", "probability": 0.90966796875}, {"start": 512.23, "end": 512.77, "word": " ุณูู", "probability": 0.5545247395833334}, {"start": 512.77, "end": 513.25, "word": " ุงูุชูุงู
ู", "probability": 0.841796875}, {"start": 513.25, "end": 513.39, "word": " ู
ู", "probability": 0.44140625}, {"start": 513.39, "end": 513.49, "word": " ุณุคุงู", "probability": 0.7237955729166666}, {"start": 513.49, "end": 513.83, "word": " Y", "probability": 0.89794921875}, {"start": 513.83, "end": 514.23, "word": " ูุฃุฌูุฒุฉ", "probability": 0.61859130859375}, {"start": 514.23, "end": 514.61, "word": " 6", "probability": 0.1689453125}, {"start": 514.61, "end": 515.51, "word": " 4T", "probability": 0.57080078125}, {"start": 515.51, "end": 516.49, "word": "-1DT", "probability": 0.6588134765625}, {"start": 516.49, "end": 516.89, "word": " ูY", "probability": 0.602294921875}, {"start": 516.89, "end": 517.09, "word": " ู
ู", "probability": 0.85595703125}, {"start": 517.09, "end": 517.37, "word": " ุณูุจ", "probability": 0.81103515625}, {"start": 517.37, "end": 517.53, "word": " Y", "probability": 0.8193359375}, {"start": 517.53, "end": 517.71, "word": " ุนูู", "probability": 0.7099609375}, {"start": 517.71, "end": 518.03, "word": " 4", "probability": 0.80712890625}, {"start": 518.03, "end": 518.23, "word": " ุนูู", "probability": 0.560546875}, {"start": 518.23, "end": 518.53, "word": " Y", "probability": 0.2353515625}, {"start": 518.53, "end": 518.67, "word": " ุนูู", "probability": 0.88916015625}, {"start": 518.67, "end": 518.97, "word": " 4", "probability": 0.95947265625}], "temperature": 1.0}, {"id": 21, "seek": 54269, "start": 519.73, "end": 542.69, "text": "ูุฐู ุงูู
ุดุชูุฉ ูู ุงูู
ุดุชูุฉ ุงูู X ุจุงููุณุจุฉ ููู Y ูู ุงููู ุจุชุทูุน ูุดุชููุง ุทุจุนุง ุงูุง ุงุณุชุฎุฏู
ุช ุงูู Fundamental Calculus ุงูุง ุนูุฏ ุงุดุชููุง ุชูุงู
ู ุจุนูุถ ุงูุญุฏูุฏ ุจุฏู ุงู T ู Y ุจุณูุท ุฌุฏุฑุณูู ุงุฑุจุนุฉ ู ูุงู ููู ูุงุญุฏ ูุงูู
ุดุชูุฉ ุงู Y ุจูุงุญุฏ ูุฅูู ู
ุง ุงูุณูุฑ ู
ุจูู ุจุฏู ูุชุงุจุน ุงูู
ุดุชูุฉ ุงูุณูุฑ ุฏู ุงููู ุงูู
ุดุชูุฉ ุงูุฑุจูุญุฉ ูู ุงูุฑุจูุญุฉ", "tokens": [3224, 24192, 9673, 8592, 2655, 28671, 39896, 9673, 8592, 2655, 28671, 2423, 39184, 1783, 20666, 1863, 35457, 3660, 24976, 39184, 398, 8032, 7578, 13672, 7578, 39894, 9566, 1211, 3615, 8717, 8592, 2655, 4587, 11296, 23032, 3555, 3615, 995, 1975, 8315, 44713, 9778, 40448, 2655, 2423, 39184, 13493, 44538, 3511, 36002, 1975, 8315, 43242, 1975, 8592, 2655, 4587, 11296, 6055, 4117, 10943, 1211, 45030, 2407, 11242, 21542, 3215, 23328, 47525, 1211, 2423, 314, 4032, 398, 4724, 3794, 1829, 9566, 10874, 3215, 2288, 3794, 1829, 4117, 1975, 25513, 27884, 4032, 36764, 1829, 8717, 4587, 1211, 36764, 24401, 6156, 45340, 8592, 2655, 28671, 2423, 398, 4724, 14407, 24401, 5296, 28814, 1829, 3224, 19446, 21136, 5172, 2288, 3714, 3555, 4587, 7578, 4724, 16254, 8717, 2655, 16758, 3615, 9673, 8592, 2655, 28671, 21136, 5172, 2288, 11778, 3224, 2423, 3224, 7578, 9673, 8592, 2655, 28671, 34892, 21292, 5016, 3660, 8032, 7578, 34892, 21292, 5016, 3660], "avg_logprob": -0.4862500041723251, "compression_ratio": 1.9518072289156627, "no_speech_prob": 0.0, "words": [{"start": 519.73, "end": 520.05, "word": "ูุฐู", "probability": 0.5350341796875}, {"start": 520.05, "end": 520.15, "word": " ุงูู
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ุดุชูุฉ", "probability": 0.9010009765625}, {"start": 537.81, "end": 538.23, "word": " ุงูุณูุฑ", "probability": 0.8089192708333334}, {"start": 538.23, "end": 538.63, "word": " ุฏู", "probability": 0.62353515625}, {"start": 538.63, "end": 538.79, "word": " ุงููู", "probability": 0.4951375325520833}, {"start": 538.79, "end": 539.41, "word": " ุงูู
ุดุชูุฉ", "probability": 0.9781494140625}, {"start": 539.41, "end": 540.61, "word": " ุงูุฑุจูุญุฉ", "probability": 0.8209228515625}, {"start": 540.61, "end": 541.75, "word": " ูู", "probability": 0.855224609375}, {"start": 541.75, "end": 542.69, "word": " ุงูุฑุจูุญุฉ", "probability": 0.672271728515625}], "temperature": 1.0}, {"id": 22, "seek": 57055, "start": 543.24, "end": 570.56, "text": "ูู
ุง ูุถูู ูุงุญุฏ ุจุชุฑูุญ ุงููู ูู ุณูุจ ูุงุญุฏ ุจุฏุฃ ุณูููุณ ุฃุฑุจุนุฉ ูุงู ุชุญุช ุงูุฌุฏุงุฑ ุจูุตูุฑ ุณูู ุชุฑุจูู ุงููุงู ูุงูุญุฏูุฏ ุจู
ุง ูู ู
ุนุชููุฉ ูู ุงูุณุคุงู ุณูุจ ุจุงู ุนูู ุฃุฑุจุน ูุจุงูู ุนูู ุฃุฑุจุน ุชูููู ุงูุฑ ุณูู ุชุฑุจูู ูู ุงูุชุงู ูุงูุญุฏูุฏ ุจุชููู ุงุชููู ูุงุฎุฏ ู
ุซู ุชุงูู find the arc length function ููุทูุจ arc length function for the graph of f of x ุชุณูู ุงุชููู", "tokens": [1211, 15042, 8717, 11242, 33911, 36764, 24401, 39894, 32887, 5016, 13672, 1829, 31439, 8608, 46152, 36764, 24401, 4724, 3215, 10721, 8608, 1829, 4117, 2407, 3794, 5551, 25513, 27884, 36764, 1829, 6055, 33753, 25724, 3215, 9640, 4724, 1829, 9381, 13546, 8608, 1829, 4117, 6055, 2288, 21292, 3224, 2423, 14407, 1829, 16070, 24401, 23328, 4724, 15042, 39896, 20449, 2655, 1863, 10632, 8978, 21136, 33604, 6027, 8608, 46152, 4724, 47302, 15844, 5551, 25513, 3615, 5296, 3555, 995, 38436, 15844, 5551, 25513, 3615, 6055, 4117, 2407, 9957, 1975, 5172, 2288, 8608, 1829, 4117, 6055, 2288, 21292, 3224, 31439, 16712, 7649, 16070, 24401, 23328, 39894, 20292, 3224, 1975, 2655, 1863, 9957, 8717, 47283, 3215, 50113, 1211, 6055, 7649, 1829, 915, 264, 10346, 4641, 2445, 8032, 1863, 9566, 46152, 10346, 4641, 2445, 337, 264, 4295, 295, 283, 295, 2031, 6055, 3794, 2407, 7578, 1975, 2655, 1863, 9957], "avg_logprob": -0.46830985264878877, "compression_ratio": 1.9147286821705427, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 543.24, "end": 543.64, "word": "ูู
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ู ุตูุฑ ููุงุญุฏ ุงู X ู
ุชุตูุฉ ุจุงูุฑุจุน ุญุจ ูุถูู ููุง ูุงุญุฏ ู ูุงุฎุฏูุง ุชุญุช ุงูุฌุฏุฑู
ู ุฃูู X ูู As of X ูุณู
ููุง ุญุณุงุจ ุงูุชูุงู
ู ู
ู ุตูุฑ ู X ูุฒูุฏ ูุงุญุฏ ุฒุงุฆุฏ ุชุณุนุฉ T ุฏู ุชุงูู ุทุจุนุง ุณู
ููุง ุงุญูุง ุจุฏู X ุณู
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ู ุนูู ุฏู ุทุจุนุง ููุญู ููุถุฉ ูุงุญุฏ ุฒู ุงูุชุณุนุฉ ุช ูุจุทูุน ุฏู ูู ุชุณูู ุชุณุนุฉ ุฏู ุช ูุงู
ุง ุชููู ุช ุชุณูู ุตูุฑ ุจุฏููู ูู ุชุณูู ูุงุญุฏ ุจุชุนูุฏูุง ุงู ูุงู
ุง ุช ุชุณูู X ุจุฏููู ูู ุชุณูู ูุงุญุฏ ุฒู ุงูุชุณุนุฉ X ูุจุทูุน ุงู ุงูุชูุงู
ู ุจุนุฏ ู
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ุน ูุฐุง ุงูุฌูุงุจ ูู ูุจููู ุงููููุง ุงููู ูู ุงูุชุทุจูู ุงูุชุงูู ููุชูุงู
ู ุงูู
ุญุฏูุฏ ุงููู ูู ุฅูุฌุงุฏ ุทูู ุงูู
ูุญูุฉ ูุฏูู ูู
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ูู ููู
ุงูุชูููู ูุงูุณูุงู
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