If $f(x)=\int_\limits 0^x \sin ^8 t \mathrm{~d} t$, then $f(x+\pi)$ equals

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

f(x)=\int\limits_{0}^x \sin ^8 t \mathrm{~d} t

, then

f(x+\pi)

equals

View answer and explanation

Correct option: C

f(x)+f(\pi)

Option C (

f(x)+f(\pi)

) is correct because

f(x+\pi)

can be split into two integrals, one from 0 to

\pi

and the other from

\pi

x+\pi

, which simplifies to

f(x)+f(\pi)

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