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int[sin(101 x)*sin^(99)x]dx...

`int[sin(101 x)*sin^(99)x]dx`

A

`(1)/(100)sin(100x)(sinx)^(100)+C`

B

`(1)/(100)cos(100x)(sinx)^(100)+C`

C

`(1)/(100)cos(100x)(cosx)^(100)+C`

D

`(1)/(100)sin(100x)(sinx)^(101)+C`

Text Solution

Verified by Experts

The correct Answer is:
a
Let `I=intsin(101x)sin^(99)x` dx . then,
`I=intsin(100x+x)sin^(99)xdx`
`rArrI=intunderset(I)(ubrace(sin(100x)))underset(II)(ubrace(cos xsin^(99)x))dx+intcos(100x) sin^(100)xdx`
`rArrI=sin(100x)((sinx)^(100))/(100)-intcos(100x)(sinx)^(100)xdx+intcos (100x)(sinx)^(100)dx+C`
`rArrI=(1)/(100)sin(100x)(sinx)^(100)+C`
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