Mathematics

Problem

Define

J_n=\displaystyle\int_{0}^{\pi/2}\sin^{n}x\,dx

for even integers

n\ge 2

. It is known that

J_n=\dfrac{n-1}{n}\,J_{n-2}

. What is

J_4

? a)

\dfrac{\pi}{4}

\dfrac{3\pi}{8}

\dfrac{3\pi}{16}

\dfrac{\pi}{8}