Expert: Paul Klarreich - 5/27/2010

Question
How would I evaluate a definite integral of an absolute trig value function?
Specifically,this one:

2π∫abs(xcos(x))dx

Evaluated from 0 to 90.

Thank You for helping.

Answer
Charles
Private: No
Subject:  
Question: How would I evaluate a definite integral of an absolute trig value function?
Specifically,this one:

2π∫abs(xcos(x))dx

Evaluated from 0 to 90.

................................

abs(something) means:

The something when the something is positive or zero.
The opposite of the something (put minus in front) when the something is negative.

So if you are doing it from 0 to pi/2 (Please!  Degrees are for children), that is all nonnegative, so:

2π∫abs(xcos(x))dx = (from 0 to pi/2)

2π∫xcos(x)dx

Now use integration by parts, etc.