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Empower And Reciprocate (Posted on 2007-11-24) Difficulty: 2 of 5
g(y) is a continuous function satisfying g(5-y) + g(y) = 0 for 0 ≤ y ≤ 5.

Evaluate:
       5
     (1+ 5g(y))-1 dy
      0

See The Solution Submitted by K Sengupta    
Rating: 3.0000 (2 votes)

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Solution Switching integral! | Comment 1 of 8

Hi!

Let make a change in the integral like this t=5-y.

So for y=0 -> t=5 and for y=5 -> t=0

dt=-dy and because g(5-y) = - g(y) the new integral is :

     5                                        5
     ç5g(y)(1+ 5g(y))-1 dy  =    5-ç(1+ 5g(y))-1 dy
      0                                       0

So I = 5-I => I=5/2

 

 

Edited on November 25, 2007, 8:02 am

Edited on November 25, 2007, 8:03 am
  Posted by Chesca Ciprian on 2007-11-24 13:29:38

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