Finding the value of integral.

  • #1
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Homework Statement


$$ \int_0^{\pi} \frac{x(sinx)^{2n}}{(sinx)^{2n}+(cosx)^{2n}} $$ =
A) π2
B) 2π2
C) π2/4
D) π/2

Homework Equations


$$ \int_0^π f(x)dx = \int_0^π f(a-x)dx $$

The Attempt at a Solution


If we put n = 1, we get the C option π2/4
But is it true for all n?
 

Answers and Replies

  • #2
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36
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.
 
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  • #3
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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.
Thanks, I got it certainly Calculus Cuthbert.:smile:
 
  • #4
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muffins from the cupboard ? no, no dear fellow I'm not hungry.
 
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