When [i][math]y[/math][/i] is written as a function of [i][math]x[/math][/i], greater values of the function are indicated by points farther away from the [math]x[/math]-axis. [br][br]When [i][math]x[/math][/i] is written as a function of [i][math]y[/math][/i] (as illustrated in this interactive figure), greater function values are indicated by points that are a greater distance from the [math]y[/math]-axis. In this figure, functions [math]f[/math] and [math]g[/math] are functions of [math]y[/math]; function [i][math]f[/math][/i] is greater than function [i][math]g[/math][/i] since [math]f[/math] is graphed further to the right. [br][br]The [b][color=#274e13]green point[/color] [/b]can be moved anywhere along the [i]y[/i]-axis from [math]y=c[/math] to [math]y=d[/math]. [br]Use the [b]slider[/b] to see a geometric visualization of the construction of a definite integral evaluated with respect to [i][math]y[/math][/i].

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