In the past, we used midpoint rule to estimate the area under a single variable function. We’d draw rectangles under the curve so that the midpoint at the top of each rectangle touched the graph of the function. Then we’d add the area of each rectangle together to find an approximation of the area under the curve. When we translate this into three-dimensional space, it means that we use three-dimensional rectangular prisms, instead of two-dimensional rectangles, to approximate the volume under a multivariable function.

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