Finding the value of integral.

1. May 13, 2015

Raghav Gupta

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. May 13, 2015

certainly

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.

3. May 13, 2015

Raghav Gupta

Thanks, I got it certainly Calculus Cuthbert.

4. May 13, 2015

certainly

muffins from the cupboard ? no, no dear fellow I'm not hungry.