Evaluate this definite integral:

pi
∫ (| |sin y| - |cos y| |) dy
0

Note: |x| denotes the absolute value of x.

The final result is  4*( sqrt(2)-1  )

You get the result by subdividing the range  into three parts:

from zero to pi/4          area=sqrt(2)-1

from pi/4  to pi/2           area=sqrt(2)-1

together                          2*( sqrt(2)-1  )

same from pi/2  to pi           area=2*( sqrt(2)-1  )

total          4*( sqrt(2)-1  )

Ady

 

 

 

 

 

Edited on July 24, 2008, 6:26 pm

Posted by Ady TZIDON on 2008-07-24 13:18:50