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

$(b-a) \int_\limits a^b f(x) d x$

$\frac{1}{2}(b-a) \int_\limits a^b f(x) d x$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

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

, then

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

is equal to

View answer and explanation

Correct option: B

\frac{1}{2}(a+b) \int\limits_{a}^b f(x) d x

Option B is correct because using the property of definite integrals

\int_a^b f(x) dx = \int_a^b f(a+b-x) dx

, we can simplify the given integral and find its value.

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