Recall that a function f is called [i]even [/i]when [math]f\left(x\right)=f\left(-x\right)[/math] for every input [i][math]x[/math][/i] in its domain.[br]Because of this, the graph of every even function has symmetry with respect to the [i][math]y[/math][/i]-axis. [br][br]Recall that a function is called [i]odd [/i]when [math]f\left(-x\right)=-f\left(x\right)[/math] for every input [i][math]x[/math][/i] in its domain. [br]Because of this, the graph of every odd function has symmetry with respect to the origin. [br][br]Because of the symmetry of even and odd functions, there are short-cut methods to computing definite integrals of these functions when the limits of integration go from [math]-a[/math] to [math]a[/math]. Can you determine these short-cut methods based on the interactive figure?

[i]Developed for use with Thomas' Calculus, published by Pearson.[/i]