If g(x)=int0^x(|sint|+|cost|)dt ,then g(...

If `g(x)=int_0^x(|sint|+|cost|)dt` ,then `g(x+(pin)/2)` is equal to, where `n in N ,` (a) `g(x)+g(pi)` (b) `g(x)+g((npi)/(2))` (c) `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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