For a double integral over a general region, [math]\int\int_Rh\left(x,y\right)dA[/math] , the region can be bound by top and bottom curves , [math]f_{bottom}\left(x\right),f_{top}\left(x\right)[/math], or left and right curves, [math]g_{left}\left(y\right),g_{right}\left(y\right)[/math]. This applet illustrates both options.[br][br]With "Bottom to Top" checked functions of [math]x[/math] define the bottom and top of the area. The integral from the bottom to top gives the integral for a [math]dx[/math] thick element which can then be integrated from left to right. Clicking the play button or moving the Left2Right slider advances the integration.[br][br]With "Left to Right" checked the region is bounded by curves on the left and right. These curves are functions of [math]y[/math]. So the integral from [math]g_{left}(y)[/math] to [math]g_{right}(y)[/math] provides the integral for a [math]dy[/math] thick slice. This can then be integrated in the [math]y[/math] direction to provide the full integral. The play button or slider can be used to illustrate the outer integral.