# Integral - help needed please

1. Jan 27, 2006

### 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!

2. Jan 27, 2006

### StatusX

Do you know what the graphs look like? Keep in mind that a positive function times a negative function is negative, etc, and the integral of a positive function is positive, etc.

3. Jan 27, 2006

### benorin

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

4. Jan 27, 2006