Question

Check my work on changing the order of integration?

\[\int\limits_{0}^{1} \int\limits_{0}^{x^3} e^{x}\sin(y)dydx\]

Answer 1

\[\int\limits_{0}^{1} \int\limits_{0}^{y^{1/3}} e^{x}\sin(y)dxdy\]

Answer 2

I just drew a picture, and since I had y=x^3 I figured solving for x gives y^(1/3) .. Am I close, or way off?

Answer 3

I guess it didn't copy well in the initial post, here is the original ntegral:

\[\int\limits_{0}^{1} \int\limits_{0}^{x^3} e^{x}\sin(y)dydx\]