Chapter 14.2, Problem 23E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Finding VolumeIn Exercises 21–26, use a double integral to find the volume of the indicated solid.

To determine

To calculate: The volume of the solid given below.

Explanation

Given:

The provided solid is:

Formula used:

The volume of a solid is provided by,

V=âˆ¬Rf(x,y)dA where, f(x,y)=z

Calculation:

The volume of a solid is provided by,

V=âˆ¬Rf(x,y)dA where, f(x,y)=z

From the figure,

f(x,y)=z=14(12âˆ’2xâˆ’3y)

Now, for the x-y plane, put z=0, and get the following,

2x+3y=12

The provided diagram is projected on x-y plane as,

Or,

y=13(12âˆ’2x)=âˆ’23x+4

So, y goes from 0 to 13(12âˆ’2x) and x goes from 0 to 6

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