# Integral - help needed please

Natasha1
I have been asked to explain without evaluating the integrals why the integral of x cos x from 0 to pi/2 is positive and the integral of x cos x from pi/2 to pi is negative. Also would I expect x cos x from 0 to pi to be positive, zero or negative? And why ?

How can I do this without evaluting it? some help would be much appreciated, thanks!

If $$f(x)\geq 0$$ for x in [a,b], then $$\int_{a}^{b}f(x)dx \geq 0$$.