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The value of int(0)^(pi) | sin^(3) theta...

The value of `int_(0)^(pi) | sin^(3) theta | d theta ` is

A

0

B

`pi`

C

`(4)/(3)`

D

`(3)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `l = int_(0)^(pi) sin^(3) theta d theta " " [ {:( :' sin theta gt 0),("for " 0 lt theta ltpi ):}]`
` = int_(0)^(pi) sin theta (1- cos^(2) theta ) d theta`
Put ` cos theta = t rArr - sin theta d theta = dt`
` :. l = -int_(1)^(-1) (1-t^(2)) dt = int_(-1)^(1) (1-t^(2))dt = [ t- (t^(3))/3]_(-1)^(1) = 2 - 2/3 = 4/3 `
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