Hello!

Can someone please tell me how to solve this double integral?

$\displaystyle \int_0^{\sqrt{\pi}} \int_x^{\sqrt{\pi}} \! 2\sin{(y^2)} \, \mathrm{d} y\mathrm{d} x$

The following hint is given: Sketch the domain of integration.

I don't know the antiderivative of $\displaystyle 2\sin{(y^2)}$. I tried to guess a couple of antiderivatives, but none of their derivatives were equal to $\displaystyle 2\sin{(y^2)}$.

Is there something else I should do first (and how)?

Thanks!

I tried switching dydx to dxdy, which results inUpdate:

$\displaystyle \int_x^{\sqrt{\pi}} \int_0^{\sqrt{\pi}} \! 2\sin{(y^2)} \, \mathrm{d} x\mathrm{d} y$

But this seems even worse, because the variable boundary is now on the outer integral.

Please help! I still can't solve this one.