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If g(x)=int0^xcos^4tdt , then g(x+pi) eq...

If `g(x)=int_0^xcos^4tdt ,` then `g(x+pi)` equals `g(x)+g(pi)` (b) `g(x)-g(pi)` `g(x)g(pi)` (d) `(g(x))/(g(pi))`

A

`(g(x))/(g(pi))`

B

`g(x)+g(pi)`

C

`g(x)-g(pi)`

D

`g(x).g(pi)`

Text Solution

Verified by Experts

The correct Answer is:
B
`g(x+pi)=int_(0)^(x+pi)cos^(4)tdt`
`=int_(0)^(pi)cos^(4)tdt+int_(x)^(x+pi)cos^(4)t dt ( :' cos^(4) t"has period" pi)`
`=g(x)+int_(0)^(pi)cos^(4)tdt`
`=g(x)+g(pi)`
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