If $f(x)=f(a-x)$, then $\int_\limits0^a x f(x) d x$ equals

$\frac{a}{2} \int_\limits0^a x f(x) d x$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

f(x)=f(a-x)

, then

\int\limits_{0}^a x f(x) d x

equals

View answer and explanation

Correct option: D

None of these

None of these is the correct option. The correct answer is

\frac{{a}}{{2}} \int_0^a f(x) dx

because using the substitution

x = a - u

and the given property

f(x) = f(a-x)

leads to this result.

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