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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!