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int cos 2x.cos 4x. Cos 6x dx is equal to...

`int cos 2x.cos 4x. Cos 6x dx` is equal to

A

`(sin12x)/(12)+(sin 8x)/(4)+(sin 4x)/(2)+C`

B

`(1)/(4)[(sin12x)/(12)+sin 8x)/(4)+(sin 4x)/(2)]+C`

C

`(1)/(4)[sin12x)/(12)+(sin 8x)/(8)+(sin 4x)/(4)]+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
`int cos 2x cos 4x cos 6x dx`
`=int cos 2x[(1)/(2){cos (4x+6x)+cos(4x-6x)}]dx`
`=(1)/(2)int[cos 2x cos 10x+cos 2x cos (-2x)]dx`
`=(1)/(2)int[cos 2x cos 10x +cos^(2)2x]dx`
`=(1)/(2)int[(1)/(2){cos(2x+10x)+cos (2x-10x)}+((1+cos 4x)/(2))]dx`
`=(1)/(4)int[cos 12x+cos 8x+1+cos 4x]dx`
`=(1)/(4)[(sin 12x)/(12)+(sin 8x)(8)+x+(sin4x)/(4)]+C`
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