I want to integrate the following function: e^(-i*(u*x+v*y)) with respect to x and y. Evaluated where x value is between -W and W, while y value is between -H and H. And i in the function is the imaginary number, while u and v are arbitrary constant variable.

I was able to get the integral itself, which evaluates to: -e ^(-i*(u*x + v*y))/(u*v)

However mathematica was able to simplify the final solution to: (4 Sin[H v] Sin[u W])/(u v)

Whereas the furthest I was able to get was: 4 * e ^ ( i * (u*w - v *h))/(uv)

Where did I go wrong? What am I missing?

Any help is greatly appreciated.

Thank you!