Odd and Even functions

**arze** · August 19th 2010, 05:56 PM

Prove that:
a) if f(x) is an even function, $\int^a_{-a}f(x)dx=2\int^a_0 f(x)dx$
b)if f(x) is an odd function, $\int^a_{-a} f(x)dx=0$

I tried using proof by contradiction:
f(x) is even, then $\int^a_{-a}f(x)dx\neq 2\int^a_0 f(x)dx$
My problem is I don't know how to continue.
I figure if I get the first one right I can do the other.
Thanks!

**Ackbeet** · August 19th 2010, 06:17 PM

You have to use the conditions on even and odd functions. I would then break up both LHS integrals into two pieces: one on either side of the origin.

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