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The value of the integral int (0)^(pi/...

The value of the integral ` int _(0)^(pi//2) (sin ^(100)x - cos^(100)x) dx ` is

A

`(1)/(100)`

B

`(100!)/((100)^(100))`

C

`(pi)/(100)`

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
` l = int _(0)^(pi//2) ( sin ^(100) x - cos^(100)x) dx `
` rArr l = uint _(0)^(pi//2) [ sin^(100) (pi/2 - x ) - cos ^(100) (pi/2 - x) dx ] ` ,
` rArr l = int _(0)^(pi//2) ( cos ^(100) x - sin ^(100) x) dx `
` rArr 2l = 0`
` rArr l = 0 `
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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