Show that, int(0)^(pi)sin^(4)xdx=2int(0)...

Show that, `int_(0)^(pi)sin^(4)xdx=2int_(0)^((pi)/(2))sin^(4)xdx`, hence, find the value of `int_(0)^(pi)sin^(4)xdx`.

Text Solution

Verified by Experts

The correct Answer is:

`(3pi)/(8)`

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int_(0)^((pi)/(2))sin^(3)xdx

Show that, int_(0)^(pi)sin^(3)xdx=2int_(0)^((pi)/(2))sin^(3)xdx and hence, find the value of int_(0)^(pi)sin^(3)xdx .

Knowledge Check

int_(0)^((pi)/(4))sec^(4)xdx

A

`(4)/(3)`

B

`(2)/(3)`

C

`(1)/(3)`

D

`(3)/(4)`

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