Evaluating Definite Integrals Using Symmetry

$f(x)$ is an even-function if $f(-x)=f(x)$

• graph of an even $f(x)$ is always symmetric about the y-axis $g(x)$ is an odd- function if $g(-x)=-g(x)$ This will help us solve these type of integrals quicker
• The graph of an odd function always has rotational symmetry of order 2 about the origin. In other words, if we rotate the graph $180^\circ$ about the origin, the resulting graph looks the same.