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If f(x) = co s x-cos^2 x + cos^3 x-....t...

If `f(x) = co s x-cos^2 x + cos^3 x-....to oo` then `int f(x) dx` is equal to

A

`tan.(x)/(2)+C`

B

`x+tan.(x)/(2)+C`

C

`x-(1)/(2)tan.(x)/(2)+C`

D

`x-tan.(x)/(2)+C`

Text Solution

Verified by Experts

The correct Answer is:
D
`because f(x)=cosx-cos^(2)x+cos^(3)x-….oo=(cosx)/(1+cosx)`
`therefore intf(x)dx=int(1+cosx)/(1+cosx)dx-int(1)/(1+cosx)dx`
`=int1dx-(1)/(2)int sec^(2).(x)/(2)dx`
`=x-(1)/(2)tan.(x)/(2).2+C=x-tan.(x)/(2)+C`
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