The value of overset(pi//2)underset(0)in...

The value of `overset(pi//2)underset(0)int x^(10) sin x" dx"`, is then the value of `mu_(10)+90mu_(8)`, is

A

`10(pi/2)^(3)`

B

`10(pi/2)^(9)`

C

`pi/2`

D

0

Text Solution

Verified by Experts

The correct Answer is:

B

Given, `l_(10)=int_(0)^(pi//2)x^(10)sinx dx`
`=[-x^(10)cosx]_(0)^(pi//2)10x^(9).cos xdx`
`=0+[10x^(9)sinx]_(0)^(pi//2)-int_(0)^(pi//2)90x^(8)sin xdx`
`=10((pi)/(2))^(9)-90l_(8)`
`rArr" "l_(10)+90l_(8)=10((pi)/(2))^(9)`

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Knowledge Check

The value of int_(0)^(pi//2) x^(10) sin x" dx" , is then the value of mu_(10)+90mu_(8) , is

A

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`9(pi/2)^(6)`

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