Worked examples

Double and triple integrals

One sheet for each type of problem, with several worked examples of increasing difficulty: first the computation, then the explanation in words. Each sheet starts with links to the theory it uses.

• 1Double integrals over rectangles
• 2Double integrals over normal domains
• 3Changing the order of integration
• 4Double integrals in polar coordinates
• 5Changes of variables with the Jacobian
• 6Triple integrals by vertical lines and by slices
• 7Triple integrals in cylindrical and spherical coordinates
• 8Volumes, masses and centroids