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Question
If \[f(-x)=-f(x)\], what is \[\int_{-a}^{a} f(x)\,dx\]?
Options
\[-\int_{0}^{a} f(x)\,dx\]
\[2\int_{0}^{a} f(x)\,dx\]
\[0\]
\[\int_{0}^{a} f(x)\,dx\]
MCQ
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Solution
The condition \[f(-x)=-f(x)\] defines an Odd Function. For symmetric limits from \[-a\] to \[a\], the integral of an odd function is zero.
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