   Chapter 15.1, Problem 39E

Chapter
Section
Textbook Problem

Find the volume of the solid lying under the elliptic paraboloid x2/4 + y2/9 + z = 1 and above the rectangle R = [−1, 1] × [−2, 2].

To determine

To find: The volume of the solid that lies under the elliptic paraboloid and above the rectangular region.

Explanation

Calculation:

Formula used:

The volume of the solid, V=RzdA .

Here, z is the given function.

Given:

The elliptic paraboloid is x24+y29+z=1 .

The rectangular region is, R=[1,1]×[2,2] .

Calculation:

Express the elliptic paraboloid as z=1x24y29 .

The volume of the solid is computed as follows.

V=RzdA=1122(1x24y29)dyd

First, compute the integral with respect to y.

V=11[yx2y4y33

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