If $f(x)=\int_\limits0^x \cos ^4 t d t$, then $f(x+\pi)$ equals

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

f(x)=\int\limits_{0}^x \cos ^4 t d t

, then

f(x+\pi)

equals

View answer and explanation

Correct option: A

f(x)+f(\pi)

Option A is correct because by using the property of definite integrals and trigonometric identities, we can show that f(x+

\pi

) = f(x) + f(

\pi

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