Evaluate the integral I=∫0π/2sin3/2(x)sin3/2(x)+cos3/2(x)dxI = \int_{0}^{\pi/2} \frac{\sin^{3/2}(x)}{\sin^{3/2}(x) + \cos^{3/2}(x)} dxI=∫0π/2sin3/2(x)+cos3/2(x)sin3/2(x)dx.
π4\frac{\pi}{4}4π
π2\frac{\pi}{2}2π
π3\frac{\pi}{3}3π
3π8\frac{3\pi}{8}83π