If $g(x)=\int_\limits 0^x \cos ^4 t \mathrm{~d} t$ then $g(x+\pi)$ equals

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Application +4 | -1

g(x)=\int\limits_{0}^x \cos ^4 t \mathrm{~d} t

then

g(x+\pi)

equals

View answer and explanation

Correct option: A

g(x)+g(\pi)

Option A (g(x)+g(π)) is correct because the integral from 0 to x+π can be split into integrals from 0 to π and π to x+π, and a substitution can be used to show the latter equals g(x).

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