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The value of int (0)^(pi//2) sin ^(8) x...

The value of ` int _(0)^(pi//2) sin ^(8) x dx ` is

A

`(105pi)/(32(4!))`

B

` (105pi)/(14(4!))`

C

` (105)/(16pi(4!))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Let `l=int_(0)^(pi//2) sin^(8) x dx = (7.5.3.1)/(8.6.4.2.2).(pi)/(2)` [By Walli's formula]
`=(105 pi)/(32(4.3.2.1))=(105 pi)/(32.4!)`
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