Well, my problem isn't with the double integral bit, it's just with the integration once I've switched the limits et cetera. The original problem is:

$\displaystyle \int_{0}^{1}\int_{\sqrt{y}}^{1}2x^5y\cos{(xy^2)}dx dy$

...and I'm told to solve it by changing the order of integration. I get:

$\displaystyle \int_{0}^{1}\int_{0}^{x^2}2x^5y\cos{(xy^2)}dydx$

I know this forum's not here to check my work, but whether my new limits are correct or not, I still don't know how to integrate $\displaystyle 2x^5y\cos{(xy^2)}$ with respect to y, taking x as a constant.

Can anyone help?