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The value (int(0)^(pi//2) (sinx)^(sqrt2+...

The value `(int_(0)^(pi//2) (sinx)^(sqrt2+1)dx)/(int_(0)^(pi//2)(sinx)^(sqrt2-1)dx)` is -

A

`(sqrt2+1)/(sqrt2-1)`

B

`(sqrt2-1)/(sqrt2+1)`

C

`(sqrt2+1)/(sqrt2)`

D

`s-sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
D
`I_(1)-overset(pi//2)underset(0)int(sin x)^(sqrt2).sin"xdx "I_(2)=overset(pi//2)underset(0)int(sin x)^(sqrt2-1)"dx"`
`I_(1)=((sinx)^(sqrt2)intsin"x dx")_(0)^(pi//2)-overset(pi//2)underset(0)int(sqrt2(sinx)^(sqrt2-1)cosx intsin"x dx")`
`=-(cos x(sinx)^(sqrt2))_(0)^(pi//2)+sqrt2overset(pi//2)underset(0)int(sinx)^(sqrt2-1)(1-sin^(2)x)dx`
`(I_(1))/(I_(2))=(sqrt2)/(1+sqrt2)xx((sqrt2-1))/((sqrt2-1))=2-sqrt2`
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