Question

Find \(\int_{0}^{\frac{\pi}{2}} sin^6(x)dx\).

(a) 0

(b) ^π⁄8

(c) ^π⁄4

(d) \(\frac{15\pi}{96}\)

I got this question by my school principal while I was bunking the class.

My doubt is from Integral Reduction Formula topic in section Integral Calculus of Engineering Mathematics

Answer 1

The correct choice is (d) \(\frac{15\pi}{96}\)

Explanation: Using the formula for even n we have

\(\int_{0}^{\frac{\pi}{2}} sin^n(x)dx=\frac{(n-1).(n-3)…3.\pi}{n.(n-2)\times …2.2}\)

We have

=\(\frac{5.3.\pi}{6.4.2.2}\)

=\(\frac{15\pi}{96}\)

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