If f(a-x) = f(x), then _0^a xf(x)dx is equal to Option 1: a/2_0^a f(x)dx Option 2: 2_0^a f(x)dx Option 3: a f(a) Option 4: a_0^a f(x)dx

The answer is 'a/2_0^a f(x)dx'. View full solution:

Calculus > Integrals

Medium

core

If $f(a-x) = f(x)$, then $\int_0^a xf(x)dx$ is equal to

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

$2\int_0^a f(x)dx$

$a f(a)$

$a\int_0^a f(x)dx$

✅ Correct Option: 1

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