The midpoint rule is a way of approximating a triple integral.
We can use a coordinate system to visualize a box with its vertex at the origin, and then we can use that coordinate system to divide the box into eight equally sized sub boxes.
The midpoint rule approximation says that the value of this integral is approximately equal to delta v, multiplied by the value of the function evaluated at each of the midpoint of the eight sub boxes.
We can approximate the value of a triple integral over a region by using the midpoint rule and dividing the region into sub boxes. We find the volume of one of the sub boxes, find the midpoint of each sub box, and then plug each midpoint into the integral we're trying to calculate.
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This video tutorial works through math problems/equations that address topics in Calculus 3, Multiple Integrals. This specific tutorial addresses Midpoint rule for triple integrals.
Length: 11 minutes
Copyright date: ©2013
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