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Ifg(x)=int0^x(|sint|+|cost|)dt ,t h e ng...

`Ifg(x)=int_0^x(|sint|+|cost|)dt ,t h e ng(x+(pin)/2)` is equal to, where `n in N ,` `g(x)+g(pi)` (b) `g(x)+g((npi)/(n2))` `g(x)+g(pi/2)` (d) none of these

A

`g(x)+g(pi)`

B

`g(x)+ng((pi)/2)`

C

`g(x)+g((pi)/2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`g(x+(pin)/2)=int_(0)^(2)(|sint|+|cost|dt`
`=int_(0)^(x)(|sint|+|cost|)dt+int_(x)^(x+(npi)/2)(|sint|+|cost|)dt`
`=g(x)=n int_(0)^(pi//2) (|sint|+|cost|)dt`
(as `|sint|+|cost|` has period `pi//2`
`=g(x)=ng((pi)/2)`
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CENGAGE-DEFINITE INTEGRATION -Exercise (Single)
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  17. A function f is defined by f(x) = int0^pi cos t cos(x-t)dt,0 <= x <= 2...

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  18. If f' is a differentiable function satisfying f(x)=int(0)^(x)sqrt(1-f^...

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