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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)`.

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We have `g(x)=int_(0)^(x)cos^(4)tdt`
`:.g(x+pi)=int_(0)^(x+pi)cos^(4)tdt`
`=int_(0)^(x)cos^(4)tdt+int_(x)^(x+pi)cos^(4)tdt`
`=g(x)+int_(0)^(pi)cos^(4)tdt [ :' "period of" cos^(4)t "is" pi]`
`=g(x)+g(pi)`
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CENGAGE ENGLISH-DEFINITE INTEGRATION -JEE ADVANCED
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