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The value of int(0)^((pi)/(8))cos^(3)4 t...

The value of `int_(0)^((pi)/(8))cos^(3)4 theta d theta` is equal to -

A

`5/3`

B

`5/4`

C

`1/3`

D

`1/6`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `l=int_(0)^(pi//8)cos^(3)4thetad theta`
`=int_(0)^(pi//8)((3cos4 theta+cos12theta)/(4))d theta`
`=(1)/(4)[(3sin4 theta)/(4)+(sin12theta)/(12)]_(0)^(pi//8)`
`=(1)/(4)[(3)/(4)("sin"(pi)/(2)-0)+(1)/(12)("sin"(3pi)/(2)-0)]`
`=(1)/(4)[(3)/(4)+(1)/(12)(-1)]=(1)/(4)((8)/(12))=(1)/(6)`
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