Q: Double integral and Fubini Compute the integral $\displaystyle\int_0^{\pi/2}\int_{\pi/2-x}^{\pi}\cos(x+y)dxdy.$
Hello, my question is that I can solve it and we have that $I=-\pi/2-1.$ But, can be that the integral let a negative value?

A: Yes an integral may be negative, and this one is so because $\cos(x+y)$ is negative in a significant subset of that interval.
