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Let nge2 be a natural number and 0ltthet...

Let `nge2` be a natural number and `0ltthetaltpi//2`. Then `int((sin^ntheta-sintheta)^(1//n)costheta)/(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

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The correct Answer is:
C
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