alleryIf $f(x)$ is an **odd** function, then $\int_{-a}^{a} f(x)\,dx$ equals:
A$2\int_0^a f(x)\,dx$
B$0$
C$\int_0^a f(x)\,dx$
D$-2\int_0^a f(x)\,dx$
Answer & Solution
Correct answer: B. $0$
For odd $f$: $f(-x) = -f(x)$, so contributions from $[-a, 0]$ and $[0, a]$ cancel exactly.
**Hence $\int_{-a}^{a} f = 0$.**
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