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

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

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

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Medium

1 of 1

Application +4 | -1

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

, then

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

View answer and explanation

Correct option: B

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

Option B (

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

) is correct because, by using the given property

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

and applying the definite integral property, the integral simplifies to

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

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