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int(0)^(pi//2)sinxsin2xdx=?...

`int_(0)^(pi//2)sinxsin2xdx=?`

A

`(2)/(3)`

B

`(3)/(4)`

C

`(5)/(6)`

D

`(3)/(5)`

Text Solution

Verified by Experts

`I=(1)/(2)int_(0)^(pi//2)[cos(2x-x)-cos(2x+x)]dx=(1)/(2)int_(0)^(pi//2)(cosx-cos3x)dx`
`=(1)/(2)[sinx-(sin3x)/(3)]_(0)^(pi//2)=(1)/(2)(1+(1)/(3))=(2)/(3)`.
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