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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 A different switch that also works | Comment 2 of 8 |
I note that g(y) is symmetric around the line y=2.5
Let x=y-2.5;    dx=dy
Limits on integral change to:

 (from -2.5 to +2.5)  (1+5^g(x))^ -1  dx
           which by symmetry is

 (from 0 to 2.5)  {(1+5^(+g(x)))^(-1)  +  (1+5^(-g(x)))^(-1) } dx
            which equals

 (from 0 to 2.5)  1  dx  =  2.5


  Posted by Larry on 2007-11-24 15:35:22
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