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If $f$ is an odd function, $\int_{-a}^a f(x)\, dx$ equals:
A$0$, since the positive and negative areas cancel by symmetry
B$2\int_0^a f$, doubling the positive half of the integral
C$2a\cdot f(a)$, treating the integral as a rectangle area
D$\int_0^a f$, halving the symmetric integral here on chart
Answer & Solution
Correct answer: A. $0$, since the positive and negative areas cancel by symmetry
For odd $f$, $\int_{-a}^a f = 0$ by symmetry.
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