g(x)=?0 to x of cos^4tdt then what is the value of g(x+p) a)g(x)+g(p) b)g(x)-G(p)

Dear Nikhil

Your question is incomplete. But I am assuming that p is period of the function here

g(x+p)=0 to x+p∫cos⁴tdt= 0 to x∫cos⁴tdt + x to x+p ∫cos⁴tdt

=g(x) + 0 to p ∫cos⁴tdt,   [using property of periods]

=g(x) + g(p)

option a

All the best.                                                           

AKASH GOYAL

AskiitiansExpert-IIT Delhi

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