Is the double integral equal to the area? I have to compute the double integral $\int_0^{\sqrt{\frac{\pi}{2}}}\int_x^{\sqrt{\frac{\pi}{2}}} 2\sin(y^2)dydx$. 
I drawed the region $0\leq x\leq \sqrt{\frac{\pi}{2}}$ and $x\leq y\leq \sqrt{\frac{\pi}{2}}$. This is a triangle with height and base equal to $\sqrt{\frac{\pi}{2}}$, right? 
The double integral is equal to the are of the triangle, or not? 
So, is the double integral equal to $\frac{1}{2}\cdot \sqrt{\frac{\pi}{2}}\cdot \sqrt{\frac{\pi}{2}}=\frac{\pi}{4}$ ?

You have a heap of sand on a triangular lot. The height of the heap at the point $(x,y)$ is defined to be $2\sin(y^2)$.  The integral you are told to compute is the volume of that heap.
