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If int0^oosinx/xdx=pi/2, then int0^oosin...

If `int_0^oosinx/xdx=pi/2`, then `int_0^oosin^3x/xdx` is equal to

A

`pi//2`

B

`pi//4`

C

`pi//6`

D

`3pi//2`

Text Solution

Verified by Experts

The correct Answer is:
B
`sin^(3)x=3/4 sinxx =1/4 sinx 3x`
`:. int_(0)^(oo) (sin^(3)x)/x dx=3/4 int_(0)^(oo) (sinx)/x dx-1/4 int_(0)^(oo) (sin 3x)/x dx`
`=3/4 int_(0)^(oo) (sinx)/x dx-1/4 int_(o)^(oo) (sinu)/u du (u=3x)`
`=3/4 (pi)/2-1/4 (pi)/2=(pi)/4`
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