Evaluate the integral I=∫0π/2sinnxsinnx+cosnxdxI = \int_0^{\pi/2} \frac{\sin^n x}{\sin^n x + \cos^n x} dxI=∫0π/2sinnx+cosnxsinnxdx for any integer nnn.
π4\frac{\pi}{4}4π
π2\frac{\pi}{2}2π
nπ4\frac{n\pi}{4}4nπ
1n\frac{1}{n}n1