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If f(x)=sinx+|sinx|andg(x)=f(x-pi)+f(x+2...

If `f(x)=sinx+|sinx|andg(x)=f(x-pi)+f(x+2pi)`, then value of `underset(-2pi)overset(5pi)(f)g(x)dx` is

A

15

B

7

C

12

D

28

Text Solution

Verified by Experts

The correct Answer is:
A

`:." "g(x)=f(x-pi)+f(x+2pi)`

`underset(-2pi)overset(5pi)(f)g(x)dx`
`:." required area"=2[2xx7]=28`.
Aliter : `g(x)=f(x-pi)+f(x+2pi)=(-sinx+|sinx|)+(sinx|sinx|)rArrg(x)=2|sinx|`
`"So, "underset(-2pi)overset(5pi)(f)g(x)dx=28`.
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