1. Estimate the volume of the following solids by Riemann sums b) The solid lying above the rectangle R = [0,2] × [0, 4] and below f(x, y) X 2. Choose the Riemann sum such that m = n = 2 and choose the points to be evaluated as the upper right corner of each partial domain.

What is Riemann Sum:

The area under the graph of a positive function on an interval can be approximated by adding the areas of rectangles whose heights are defined by the curve in single-variable calculus. Typically, the interval was divided into smaller sub-intervals, rectangles were drawn to represent the area under the curve on each of these smaller sub-intervals, and the sum of these areas was used to indicate the area under the curve. This approach can be extended to the three-dimensional counterparts of double Riemann sums and double integrals over rectangles.

Given:

A solid is given that lies below $f\left(x,y\right)=4-x-y^2$ and above the rectangle $D=\left[0,2\right]\times \left[0,4\right]$.

To Determine:

We determine the volume of the solid using upper left corner rule Riemann sum.