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If $f(x)$ is an **even** function, then $\int_{-a}^{a} f(x)\,dx$ equals:
A$0$
B$\int_0^a f(x)\,dx$
C$2\int_0^a f(x)\,dx$
D$-2\int_0^a f(x)\,dx$
Answer & Solution
Correct answer: C. $2\int_0^a f(x)\,dx$
For even $f$: $f(-x) = f(x)$, so the contributions from $[-a, 0]$ and $[0, a]$ are equal. Thus $\int_{-a}^{a} f = 2\int_0^a f$.
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