If a function [math]f[/math] has symmetry, say, if it's an even or odd function, then we can take advantage of that symmetry when integrating [math]f[/math].[br][list][*]If [math]f[/math] is an [b]even[/b] function, then it is symmetric across the [math]y[/math]-axis. We find[/*][/list] [math]\int_{-a}^af\left(x\right)dx=2\int_0^af\left(x\right)dx[/math].[br][list][*]If [math]f[/math] is an [b]odd[/b] function, then it is symmetric about the origin. We find[/*][/list] [math]\int_{-a}^af\left(x\right)dx=0[/math].[br]In the figure, drag the blue control points to reshape the graph. Once the integral is displayed, you can drag the green point on the [math]x[/math]-axis to change the value of [math]a[/math].