Even and Odd Functions : This is the final topic that we have to discuss in this chapter.
Firstly, an even function is any function which satisfies,
f ( x ) = x2
Typical examples of even functions are following,
f ( x ) = f ( x ) f ( x ) = cos (x )
An odd function is any function that satisfies,
f (- x ) = - f ( x )
The typical examples of odd functions are following,
f ( x ) = x3 f (x ) = sin ( x )
There are some nice facts regarding integrating even & odd functions over the interval [-a,a]. If f(x) is an even function then,
∫a (-a) f ( x ) dx = 2∫a0 f ( x ) dx
Similarly, if f(x) is an odd function then,
∫a (-a) f ( x ) dx =0
Note as well that in order to use these facts the limit of integration has to be the same number, however opposite signs!