Understanding the Sign of Integrals: Explaining x cos x without Evaluation

[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!

 

[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.

 

[benorin]

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

 

[VietDao29]

Do not double-post, please.
Haven't you got enough information on this page (you posted it 3 days ago remember?)? If you have any further questions, why don't consider to post it there, instead of starting a brand new thread?
This proves that some never read the hints in the posts others have given, and think about it, instead, they are looking for a complete solution!