First slide

Methods of integration

Question

$If I_{n} = \int \sin^{n} x d x then I_{8} - \frac{7}{8} I_{6} is$

Moderate

A

$\frac{\cos x \sin^{7} x}{8}$
B

$\frac{- \cos x \sin^{7} x}{8}$
C

$\frac{\sin x \cos^{7} x}{8}$
D

$- \frac{\sin x \cos^{7} x}{8}$

Solution

$I_{n} = \frac{- \sin^{n - 1} x \cos x}{n} + \frac{n - 1}{n} I_{n - 2}$
put, n = 8

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