If $f(a+b-x)=f(x)$ then $\int_\limits a^b x f(x) d x$ is equal to

$\frac{a+b}{2} \int_\limits a^b f(a+b+x) d x$

$\frac{a+b}{2} \int_\limits a^b f(b-x) d x$

$\frac{b-a^b}{2} \int_\limits a^b f(x) d x$.

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

f(a+b-x)=f(x)

then

\int\limits_{a}^b x f(x) d x

is equal to

View answer and explanation

Correct option: C

\frac{a+b}{2} \int\limits_{a}^b f(x) d x

Option C (

\frac{{a+b}}{2} \int_a^b f(x) dx

) is correct because using the given property simplifies the integral.

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