Question

If \[f(-x)=-f(x)\], what is \[\int_{-a}^{a} f(x)\,dx\]?

विकल्प

• \[-\int_{0}^{a} f(x)\,dx\]

• \[2\int_{0}^{a} f(x)\,dx\]

• \[0\]

• \[\int_{0}^{a} f(x)\,dx\]

Answer 1

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.