### Definite integral of an odd function

http://integralcalc.com/ Learn how to calculate the definite integral of an odd function. If the range of the definite integral is -a to a, and if the function is odd, then the value of the integral is 0. To determine if the function is odd, plug -x in for x, and then simplify. If the result is -f(x), then the function is odd. Since the integral is supposed to be evaluated from -a to a, and that the function is odd, you know that the function is symmetric about the origin, and therefore that the positive area will cancel out the negative area and that the value of the integral will be 0.

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