1. Estimate the volume of the following solids by Riemann sums m a) The solid lying below f(x, y) = 2cos(xy) and above the rectangle D = [0, π/2] x [0,T/2]. Choose the Riemann sum such that m = n = 2 and choose the point to be evaluated as the upper left corner of each partial domain.
![1. Estimate the volume of the following solids by Riemann sums m
a) The solid lying below f(x, y) = 2cos(xy) and above the rectangle D = [0,TT/2]
x [0,TT/2]. Choose the Riemann sum such that m = n = 2 and
choose the point to be evaluated as the upper left corner of each partial
domain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F526a6d9d-32b7-4f2d-90af-ff9540132ca2%2F2bbfea53-a85a-4eb3-be03-f8456359a68e%2F3qp8p26_processed.jpeg&w=3840&q=75)
What is Riemann Sum:
Remember how, in single-variable calculus, we added the areas of rectangles whose heights are defined by the curve to approximate the area under the graph of a positive function on an interval? The typical procedure entailed breaking the interval into smaller sub-intervals, drawing rectangles to represent the region under the curve on each of these smaller sub-intervals, and then summing the areas of these rectangles to represent the area under the curve. We can expand this method to include double Riemann sums and double integrals over rectangles, which are their three-dimensional equivalents.
Given:
A solid is given that lies below and above the rectangle .
To Determine:
We determine the volume of the solid using upper left corner rule Riemann sum.
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