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Let n ge 2 be a natural number and 0 lt ...

Let `n ge 2` be a natural number and `0 lt theta lt (pi)/(2)`, Then, `int ((sin^(n)theta - sin theta)^(1/n) cos theta)/(sin^(n+1) theta)d theta` is equal to (where C is a constant of integration)

A

`n/(n^2-1)(1-1/(sin^(n+1)theta))^((n+1)/n)+C`

B

`n/(n^2+1)(1-1/(sin^(n-1)theta))^((n+1)/n)+C`

C

`n/(n^2-1)(1-1/(sin^(n-1)theta))^((n+1)/n)+C`

D

`n/(n^2-1)(1+1/(sin^(n-1)theta))^((n+1)/n)+C`

Text Solution

Verified by Experts

The correct Answer is:
C
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