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If g(x)=int(0)^(x)cos^(4)t dt, then prov...

If `g(x)=int_(0)^(x)cos^(4)t dt`, then prove that `g(x+pi)=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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