I = ∫∫R (x + y)dA where R is the region bounded by the curve y = x² and the line y = 1.
(a) Calculate I by integrating first in y and then in x.
(b) Calculate I by integrating first in x and then in y.
This is what I got for (a): Limits for y are x² =< y =< 1, making this a parabola from origin to y=1. solving x²=1 (upper limit of y) gives the limits for x -1=<x=<1.
which I hope is correct!
I'm stuck on (b)
What should I make the limits of x & y to?
are the limits for x: ? This is from solving x² = y, making
But what do I make the limits for y? If I use I get a different answer from (a). I get 13/20.
where am I going wrong?