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## Homework Statement

Suppose f is a continuous function defined on an interval [-a, a]. Show that if f is odd, then

[itex] [-a,a]\int f(x)\,dx = 0 [/itex]

## Homework Equations

If f is odd, then

##f(-x) = -f(x)##

##u=-x##

Our TA told us to set u equal to -x.

## The Attempt at a Solution

## u = -x ##

## -du = dx ##

##-[a,-a]\int f(x)\,dx##

##[a,-a]\int -f(x)\,dx##

definition of odd function

##[a,-a]\int f(-x)\,dx##

##-\int f(u)\,du##

##-F(-x)|[a,-a]##

##F(-x)|[-a,a]##

##F(-a) - F(-(-a))##

##F(-a) - F(a)##

## -2F(a) ##

Obviously I went wrong in my proof somewhere or I got distracted and did useless steps.

Thanks in advance!