Question

How do I reverse the order of integration of the following double integral:

Answer 1

bring it on. you should always draw the area btw

Answer 2

\[\int\limits_{0}^{1}\int\limits_{0}^{x} 1-x^2 dydx\] I guessed it would simply be to change the bound to:
\[\int\limits_{0}^{1}\int\limits_{0}^{y}dxdy\]

Answer 3

(same function in the second integral)

Answer 4

The region is basically the triangle bounded by 0<x<1 and the straight line y=x

Answer 5

that is right. the way i do it is by drawing it:


then i look at it sideways

y is bounded between x = 0 and x = 1 : 0 < y < 1
and y is bounded between y = x and y = 1: x < y < 1

Answer 6

lol i just wrote same bounds twice

Answer 7

second on is: x between y and 1 y < x < 1

sorry about that

Answer 8

I messed up the bounds, but I understand now. Thank you!