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{"segments": [{"id": 1, "seek": 3054, "start": 1.58, "end": 30.54, "text": "ุจุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุฃุนุฒุงุก ุงู„ุทู„ุงุจ ุงู„ุณู„ุงู… ุนู„ูŠูƒู… ูˆุฑุญู…ุฉ ุงู„ู„ู‡ ูˆุจุฑูƒุงุชู‡ ููŠ ู‡ุฐุง ุงู„ููŠุฏูŠูˆ ุณู†ุดู‡ุฑ ุงู† ุดุงุก ุงู„ู„ู‡ ุชุทุจูŠู‚ ุงู„ุชุงู†ูŠ ู„ู„ุชูƒุงู…ู„ ุงู„ู…ุญุฏูˆุฏ ู‡ูˆ section 6 3 ุจุนู†ูˆุงู† arc length ุณู†ุนุฑู ูƒูŠู ู†ุญุณุจ ุทูˆู„ ุงู„ู…ู„ุญู†ุฉ ุจุงุณุชุฎุฏุงู… ุงู„ุชูƒุงู…ู„ ุงู„ู…ุญุฏูˆุฏ ู„ูˆ ุฃู†ุง ุนู†ุฏูƒ .. ูƒู…ุง ุชุดูˆููˆู† ููŠ ุงู„ุดูƒู„ ู‡ุฐุง ุฏุงู„ุฉ ุจู„ูˆู† ุฃุฒุฑู‚ ูุจู†ุนุฑู ูƒุฏู‡ ุทูˆู„ ุงู„ู…ู„ุญู†ุฉ ู‡ุฐุง ุงู„ู„ูŠ ู‡ูˆ ุจู„ูˆู† ุฃุฒุฑู‚ ุนู„ู‰ ุงู„ูุชุฑุฉ 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, 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A", "probability": 0.9248046875}, {"start": 30.02, "end": 30.54, "word": " ู„B", "probability": 0.708251953125}], "temperature": 1.0}, {"id": 2, "seek": 5739, "start": 33.09, "end": 57.39, "text": "ุงู„ุชุนุฑูŠู ู…ูˆุฌูˆุฏ ู‚ุฏุงู…ู†ุง Definition if f' is continuous on the closed interval a ูˆb ุงูˆู„ ุดุฑุท ุงู† ุชูƒูˆู† ุงู„ุฏุงู„ุฉ ู‚ุจู„ ุงู„ุงุดุชุบุงู„ ูˆู…ุณุชู‚ู„ู‡ุง ู…ุชุตู„ุฉ ุนู„ู‰ ุงู„ูุชุฑุฉ ู…ู† a ุงู„ู‰ b Then the length ุทูˆู„ ุงู„ุงุฑูƒ ุทูˆู„ ุงู„ู…ู„ุญู†ุฉ ุนู„ู†ุง of the curve y ุจูŠุณุงูˆูŠ 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, 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ู†ุถูŠูู‡ ู…ุน ุงู„ูˆุงุญุฏ ูˆ ุจุนุฏูŠู† ู†ุนู…ู„ ุงุฎุชุตุงุฑุงุช ูˆ ุงุฐุง ูƒุงู† ู…ูˆุฌูˆุฏ ูู†ุงุฎุฏ ุฌุฐุฑ ุงู„ุชุฑุจูŠุนูŠ ุฎุจุฑุฉ ูƒุงู…ู„ ุนุฑูู‡ุง ู…ู† A ู„ B ู‡ู†ุงุฎุฏ ุงูˆู„ ู…ุซุงู„ example find the length of the curve Y ุจูŠุณูˆุก 4 ููŠ ุฌุฐุฑ 2 ุนู„ู‰ 3 X ุงูˆ 3 ุน 2 ู†ู‚ุต 1 ูˆ X ู…ู† 0 ู„ 1 ู‡ุงูŠ ุงู„ Y ุนู†ุฏู†ุง ุจูŠุฌูŠุจ ุงู„ู…ุดุชู‚ุฉ ุงู„ุฃูˆู„ู‰ ุงู„ู…ุดุชู‚ุฉ ุงู„ุฃูˆู„ู‰ ุงู„ู„ูŠ ู‡ูŠ Y run dy dx ุจูŠุณูˆุก 2 ุฌุฐุฑ 2 ููŠ X ู†ุตู ูˆ ุชู„ุงุญุธูˆุง ุงู†ู†ุง ู…ุชุตู„ ุน ุงู„ูุชุฑุฉ ู…ู† 0 ู„ 1", "tokens": [3224, 2407, 34892, 21292, 3615, 11331, 995, 12610, 8717, 11242, 33911, 3224, 20449, 2423, 14407, 24401, 4032, 39182, 9957, 8717, 25957, 1211, 1975, 46456, 9381, 9640, 9307, 4032, 1975, 15730, 25961, 3714, 29245, 23328, 6156, 1863, 47283, 3215, 10874, 8848, 2288, 16712, 2288, 21292, 3615, 1829, 16490, 3555, 25720, 9122, 10943, 1211, 6225, 28480, 11296, 9154, 316, 5296, 363, 8032, 1863, 47283, 3215, 1975, 12610, 50113, 6027, 1365, 915, 264, 4641, 295, 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