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Absolutely Different (Posted on 2008-07-24) Difficulty: 2 of 5
Evaluate this definite integral:

pi
∫ (| |sin y| - |cos y| |) dy
0

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

See The Solution Submitted by K Sengupta    
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Solution divide et impera | Comment 3 of 5 |

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

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