What does it mean for a integrand to be an odd function?
- Saturday Dec 5,2009 08:00 PM
- By diddy
- In Others
What defines an integrand to be an odd function? One of the solutions to my calculus problems states that the integral is 0 because it is an odd function. I’m not sure what this means.
Calculus Problems, Integrand, Odd Function, Sure What This Means, What This Means
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An odd function, by definition has the property that f(x) = -f(x). When you integrate such a function with a lower bound that is negative and an upper bound that is positive, the results (areas) will cancel out. Try it with f(x) = x^3 to see this.
? x^3 dx evaluated from -2 to 2.
(x^4)/4 evaluated from -2 to 2.
[16/4 - 16/4] = 0.
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