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Find the volume of the solid bounded above by the surface $z=f(x, y)$ and below by the region $R$ in the $x$ -y plane. $f(x, y)=6, R$ rectangle determined by $1 \leq x \leq 3,2 \leq y \leq 5$.

$$36$$

Calculus 3

Chapter 6

An Introduction to Functions of Several Variables

Section 6

Double Integrals

Partial Derivatives

Campbell University

Oregon State University

Harvey Mudd College

Idaho State University

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For this problem, we are asked to find the volume of the solid bounded above by the surface. Z equals six and below by the region or below by the rectangle determined by X between one and three and why? Between two and five. So we're integrating or we're finding the double integral from 1 to 3 From 2 to 5 of six dy Dx. So we can see that this would then just be six times the integral from 1 to 3 times the integral from 2 to 5 dy Dx. So this would then be six times the integral from 1 to 3 of three dx, which would then be six times three times two, which gives us the result, well six m six, Giving us that the volume will be 36.

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