Math Insight

Applet: Region bounded by paraboloids demonstrating the shadow method

The region $\dlv$ is bounded by the elliptic paraboloids $y=5-4 x^2-z^2$ and $y=x^2+z^2/4$. If the sun is viewed to be in the direction of the positive $y$-axis, the shadow of $\dlv$ in a plane perpendicular to the $y$-axis is the region inside the ellipse $x^2+z^2/4=1$.

Applet links

This applet is found in the pages

• The shadow method for determining triple integral bounds

List of all applets

Notation systems

Select a notation system:
default Marsden and Tromba Stewart

More information on notation systems

General information about three.js applets

The applet was made using three.js and requires Javascript as well as a browser that supports WebGL. For most three.js applets, you can drag with the mouse to rotate the view, drag with the right button to pan, and zoom in/out with the mouse wheel. Many applets contain points that you can drag to change values of variables.