Define for even integers

MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals

Problem

Define Jn=∫0π/2sin⁡nx dxJ_n=\displaystyle\int_{0}^{\pi/2}\sin^{n}x\,dx for even integers n≥2n\ge 2. It is known that Jn=n−1n Jn−2J_n=\dfrac{n-1}{n}\,J_{n-2}. What is J4J_4? (a) π4\dfrac{\pi}{4} (b) 3π8\dfrac{3\pi}{8} (c) 3π16\dfrac{3\pi}{16} (d) π8\dfrac{\pi}{8}

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