Posts tagged triple integrals
Solving triple integrals using the midpoint rule

Similarly to the way we used midpoints to approximate single integrals by taking the midpoint at the top of each approximating rectangle, and to the way we used midpoints to approximate double integrals by taking the midpoint at the top of each approximating prism, we can use midpoints to approximate a triple integral by taking the midpoint of each sub-cube.

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Cylindrical coordinates and triple integrals

Like cartesian (or rectangular) coordinates and polar coordinates, cylindrical coordinates are just another way to describe points in three-dimensional space. Cylindrical coordinates are exactly the same as polar coordinates, just in three-dimensional space instead of two-dimensional space.

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Six ways to write the same iterated triple integral

There are six ways to express an iterated triple integral. While the function inside the integral always stays the same, the order of integration will change, and the limits of integration will change to match the order.

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