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Finding the value of integral.

  1. May 13, 2015 #1
    1. The problem statement, all variables and given/known data
    $$ \int_0^{\pi} \frac{x(sinx)^{2n}}{(sinx)^{2n}+(cosx)^{2n}} $$ =
    A) π2
    B) 2π2
    C) π2/4
    D) π/2
    2. Relevant equations
    $$ \int_0^π f(x)dx = \int_0^π f(a-x)dx $$

    3. The attempt at a solution
    If we put n = 1, we get the C option π2/4
    But is it true for all n?
     
  2. jcsd
  3. May 13, 2015 #2
    Remember that ##\int_0^{2a} f(x)dx=2\int_0^a f(x)dx## iff ##f(2a-x)=f(x)## and then consider the integral ##\int_0^{\pi} \frac{(sinx)^{2n}}{(sinx)^{2n}+(cosx)^{2n}}## using the rule you mentioned.
     
  4. May 13, 2015 #3
    Thanks, I got it certainly Calculus Cuthbert.:smile:
     
  5. May 13, 2015 #4
    muffins from the cupboard ? no, no dear fellow I'm not hungry.
     
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