BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Solutions

Chapter
Section
BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

Finding the Volume of a Solid Region In Exercises 21-24, use a double integral to find the volume of the solid region bounded by the graphs of the equations. See Example 3.

z   =   x y ,   z =   0 , y   =   2 x ,   y =   0 , x =   0 , x =   3

To determine

To calculate: The volume of solid region bounded by the graph of the equations. z=xy, z=0, y=2x, y=0, x=0, x=3

Explanation

Given information:

The provided equation is

z=xy, z=0, y=2x, y=0, x=0, x=3

Formula used:

The procedure to calculate volume of surface z=f(x,y),

Step-1: Write the equation of surface in the form z=f(x,y)

Step-2: Sketch the projected region R in the x-y-plane.

Step-3: Determine the order of limits of integration.

Step-4: Evaluate the volume of solid region,

Volume=mnabf(x,y)dxdy

Here, the projected region is R:

myn and axb

Calculation:

Consider equation of solid region,

z=xy, z=0, y=2x, y=0, x=0, x=3

The equation of upper solid region is

z=xy

The region R is bounded by y=2x, y=0, x=0, x=3,

The following table shown different coordinate of (x,y) for y=2x.

x-Coordinate y-Coordinate (x,y) Coordinate
0 0 (0,0)
3 6 (3,6)

The graph of region bounded by y=2x, y=0, x=0, x=3

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started
Sect-7.1 P-4SWUSect-7.1 P-5SWUSect-7.1 P-6SWUSect-7.1 P-7SWUSect-7.1 P-8SWUSect-7.1 P-1ESect-7.1 P-2ESect-7.1 P-3ESect-7.1 P-4ESect-7.1 P-5ESect-7.1 P-6ESect-7.1 P-7ESect-7.1 P-8ESect-7.1 P-9ESect-7.1 P-10ESect-7.1 P-11ESect-7.1 P-12ESect-7.1 P-13ESect-7.1 P-14ESect-7.1 P-15ESect-7.1 P-16ESect-7.1 P-17ESect-7.1 P-18ESect-7.1 P-19ESect-7.1 P-20ESect-7.1 P-21ESect-7.1 P-22ESect-7.1 P-23ESect-7.1 P-24ESect-7.1 P-25ESect-7.1 P-26ESect-7.1 P-27ESect-7.1 P-28ESect-7.1 P-29ESect-7.1 P-30ESect-7.1 P-31ESect-7.1 P-32ESect-7.1 P-33ESect-7.1 P-34ESect-7.1 P-35ESect-7.1 P-36ESect-7.1 P-37ESect-7.1 P-38ESect-7.1 P-39ESect-7.1 P-40ESect-7.1 P-41ESect-7.1 P-42ESect-7.1 P-43ESect-7.1 P-44ESect-7.2 P-1CPSect-7.2 P-2CPSect-7.2 P-3CPSect-7.2 P-1SWUSect-7.2 P-2SWUSect-7.2 P-3SWUSect-7.2 P-4SWUSect-7.2 P-5SWUSect-7.2 P-6SWUSect-7.2 P-1ESect-7.2 P-2ESect-7.2 P-3ESect-7.2 P-4ESect-7.2 P-5ESect-7.2 P-6ESect-7.2 P-7ESect-7.2 P-8ESect-7.2 P-9ESect-7.2 P-10ESect-7.2 P-11ESect-7.2 P-12ESect-7.2 P-13ESect-7.2 P-14ESect-7.2 P-15ESect-7.2 P-16ESect-7.2 P-17ESect-7.2 P-18ESect-7.2 P-19ESect-7.2 P-20ESect-7.2 P-21ESect-7.2 P-22ESect-7.2 P-23ESect-7.2 P-24ESect-7.2 P-25ESect-7.2 P-26ESect-7.2 P-27ESect-7.2 P-28ESect-7.2 P-35ESect-7.2 P-36ESect-7.2 P-37ESect-7.2 P-38ESect-7.2 P-39ESect-7.2 P-40ESect-7.2 P-41ESect-7.2 P-42ESect-7.2 P-43ESect-7.2 P-44ESect-7.2 P-45ESect-7.2 P-46ESect-7.2 P-47ESect-7.2 P-48ESect-7.2 P-49ESect-7.2 P-50ESect-7.2 P-51ESect-7.3 P-1CPSect-7.3 P-2CPSect-7.3 P-3CPSect-7.3 P-4CPSect-7.3 P-5CPSect-7.3 P-1SWUSect-7.3 P-2SWUSect-7.3 P-3SWUSect-7.3 P-4SWUSect-7.3 P-5SWUSect-7.3 P-6SWUSect-7.3 P-7SWUSect-7.3 P-8SWUSect-7.3 P-9SWUSect-7.3 P-10SWUSect-7.3 P-1ESect-7.3 P-2ESect-7.3 P-3ESect-7.3 P-4ESect-7.3 P-5ESect-7.3 P-6ESect-7.3 P-7ESect-7.3 P-8ESect-7.3 P-9ESect-7.3 P-10ESect-7.3 P-11ESect-7.3 P-12ESect-7.3 P-13ESect-7.3 P-14ESect-7.3 P-15ESect-7.3 P-16ESect-7.3 P-17ESect-7.3 P-18ESect-7.3 P-19ESect-7.3 P-20ESect-7.3 P-21ESect-7.3 P-22ESect-7.3 P-23ESect-7.3 P-24ESect-7.3 P-25ESect-7.3 P-26ESect-7.3 P-27ESect-7.3 P-28ESect-7.3 P-29ESect-7.3 P-30ESect-7.3 P-31ESect-7.3 P-32ESect-7.3 P-33ESect-7.3 P-34ESect-7.3 P-35ESect-7.3 P-36ESect-7.3 P-37ESect-7.3 P-38ESect-7.3 P-39ESect-7.3 P-40ESect-7.3 P-41ESect-7.3 P-42ESect-7.3 P-43ESect-7.3 P-44ESect-7.3 P-45ESect-7.3 P-46ESect-7.3 P-47ESect-7.3 P-48ESect-7.3 P-49ESect-7.3 P-50ESect-7.3 P-51ESect-7.3 P-53ESect-7.3 P-54ESect-7.3 P-55ESect-7.4 P-1CPSect-7.4 P-2CPSect-7.4 P-3CPSect-7.4 P-4CPSect-7.4 P-5CPSect-7.4 P-6CPSect-7.4 P-7CPSect-7.4 P-1SWUSect-7.4 P-2SWUSect-7.4 P-3SWUSect-7.4 P-4SWUSect-7.4 P-5SWUSect-7.4 P-6SWUSect-7.4 P-7SWUSect-7.4 P-8SWUSect-7.4 P-9SWUSect-7.4 P-10SWUSect-7.4 P-1ESect-7.4 P-2ESect-7.4 P-3ESect-7.4 P-4ESect-7.4 P-5ESect-7.4 P-6ESect-7.4 P-7ESect-7.4 P-8ESect-7.4 P-9ESect-7.4 P-10ESect-7.4 P-11ESect-7.4 P-12ESect-7.4 P-13ESect-7.4 P-14ESect-7.4 P-15ESect-7.4 P-16ESect-7.4 P-17ESect-7.4 P-18ESect-7.4 P-19ESect-7.4 P-20ESect-7.4 P-21ESect-7.4 P-22ESect-7.4 P-23ESect-7.4 P-24ESect-7.4 P-25ESect-7.4 P-26ESect-7.4 P-27ESect-7.4 P-28ESect-7.4 P-29ESect-7.4 P-30ESect-7.4 P-31ESect-7.4 P-32ESect-7.4 P-33ESect-7.4 P-34ESect-7.4 P-35ESect-7.4 P-36ESect-7.4 P-37ESect-7.4 P-38ESect-7.4 P-39ESect-7.4 P-40ESect-7.4 P-41ESect-7.4 P-42ESect-7.4 P-43ESect-7.4 P-44ESect-7.4 P-45ESect-7.4 P-46ESect-7.4 P-47ESect-7.4 P-48ESect-7.4 P-49ESect-7.4 P-50ESect-7.4 P-51ESect-7.4 P-52ESect-7.4 P-53ESect-7.4 P-54ESect-7.4 P-55ESect-7.4 P-56ESect-7.4 P-57ESect-7.4 P-58ESect-7.4 P-59ESect-7.4 P-60ESect-7.4 P-61ESect-7.4 P-62ESect-7.4 P-63ESect-7.4 P-64ESect-7.4 P-65ESect-7.4 P-66ESect-7.4 P-67ESect-7.4 P-68ESect-7.4 P-69ESect-7.4 P-71ESect-7.4 P-72ESect-7.4 P-73ESect-7.5 P-1CPSect-7.5 P-2CPSect-7.5 P-3CPSect-7.5 P-4CPSect-7.5 P-5CPSect-7.5 P-1SWUSect-7.5 P-2SWUSect-7.5 P-3SWUSect-7.5 P-4SWUSect-7.5 P-5SWUSect-7.5 P-6SWUSect-7.5 P-7SWUSect-7.5 P-8SWUSect-7.5 P-9SWUSect-7.5 P-10SWUSect-7.5 P-11SWUSect-7.5 P-12SWUSect-7.5 P-13SWUSect-7.5 P-14SWUSect-7.5 P-1ESect-7.5 P-2ESect-7.5 P-3ESect-7.5 P-4ESect-7.5 P-5ESect-7.5 P-6ESect-7.5 P-7ESect-7.5 P-8ESect-7.5 P-9ESect-7.5 P-10ESect-7.5 P-11ESect-7.5 P-12ESect-7.5 P-13ESect-7.5 P-14ESect-7.5 P-15ESect-7.5 P-16ESect-7.5 P-17ESect-7.5 P-18ESect-7.5 P-19ESect-7.5 P-20ESect-7.5 P-21ESect-7.5 P-22ESect-7.5 P-23ESect-7.5 P-24ESect-7.5 P-25ESect-7.5 P-26ESect-7.5 P-27ESect-7.5 P-28ESect-7.5 P-29ESect-7.5 P-30ESect-7.5 P-31ESect-7.5 P-32ESect-7.5 P-33ESect-7.5 P-34ESect-7.5 P-35ESect-7.5 P-36ESect-7.5 P-37ESect-7.5 P-38ESect-7.5 P-39ESect-7.5 P-40ESect-7.5 P-41ESect-7.5 P-42ESect-7.5 P-43ESect-7.5 P-44ESect-7.5 P-45ESect-7.5 P-46ESect-7.5 P-47ESect-7.5 P-48ESect-7.5 P-49ESect-7.5 P-50ESect-7.5 P-51ESect-7.5 P-53ESect-7.5 P-54ESect-7.5 P-55ESect-7.5 P-56ESect-7.5 P-1QYSect-7.5 P-2QYSect-7.5 P-3QYSect-7.5 P-4QYSect-7.5 P-5QYSect-7.5 P-6QYSect-7.5 P-7QYSect-7.5 P-8QYSect-7.5 P-9QYSect-7.5 P-10QYSect-7.5 P-11QYSect-7.5 P-12QYSect-7.5 P-13QYSect-7.5 P-14QYSect-7.5 P-15QYSect-7.5 P-16QYSect-7.5 P-17QYSect-7.5 P-18QYSect-7.5 P-19QYSect-7.5 P-20QYSect-7.5 P-21QYSect-7.5 P-22QYSect-7.5 P-23QYSect-7.5 P-24QYSect-7.5 P-25QYSect-7.5 P-26QYSect-7.6 P-1CPSect-7.6 P-2CPSect-7.6 P-3CPSect-7.6 P-4CPSect-7.6 P-1SWUSect-7.6 P-2SWUSect-7.6 P-3SWUSect-7.6 P-4SWUSect-7.6 P-5SWUSect-7.6 P-6SWUSect-7.6 P-7SWUSect-7.6 P-8SWUSect-7.6 P-9SWUSect-7.6 P-10SWUSect-7.6 P-1ESect-7.6 P-2ESect-7.6 P-3ESect-7.6 P-4ESect-7.6 P-5ESect-7.6 P-6ESect-7.6 P-7ESect-7.6 P-8ESect-7.6 P-9ESect-7.6 P-10ESect-7.6 P-11ESect-7.6 P-12ESect-7.6 P-13ESect-7.6 P-14ESect-7.6 P-15ESect-7.6 P-16ESect-7.6 P-17ESect-7.6 P-18ESect-7.6 P-19ESect-7.6 P-20ESect-7.6 P-21ESect-7.6 P-22ESect-7.6 P-23ESect-7.6 P-24ESect-7.6 P-25ESect-7.6 P-26ESect-7.6 P-27ESect-7.6 P-28ESect-7.6 P-29ESect-7.6 P-30ESect-7.6 P-31ESect-7.6 P-32ESect-7.6 P-33ESect-7.6 P-34ESect-7.6 P-35ESect-7.6 P-36ESect-7.6 P-37ESect-7.6 P-38ESect-7.6 P-39ESect-7.6 P-40ESect-7.6 P-41ESect-7.6 P-42ESect-7.6 P-43ESect-7.6 P-44ESect-7.6 P-45ESect-7.7 P-1CPSect-7.7 P-2CPSect-7.7 P-3CPSect-7.7 P-1SWUSect-7.7 P-2SWUSect-7.7 P-3SWUSect-7.7 P-4SWUSect-7.7 P-5SWUSect-7.7 P-6SWUSect-7.7 P-7SWUSect-7.7 P-8SWUSect-7.7 P-1ESect-7.7 P-2ESect-7.7 P-3ESect-7.7 P-4ESect-7.7 P-5ESect-7.7 P-6ESect-7.7 P-7ESect-7.7 P-8ESect-7.7 P-9ESect-7.7 P-10ESect-7.7 P-11ESect-7.7 P-12ESect-7.7 P-13ESect-7.7 P-14ESect-7.7 P-15ESect-7.7 P-16ESect-7.7 P-17ESect-7.7 P-18ESect-7.7 P-19ESect-7.7 P-20ESect-7.7 P-21ESect-7.7 P-22ESect-7.7 P-23ESect-7.7 P-24ESect-7.7 P-25ESect-7.7 P-26ESect-7.7 P-27ESect-7.7 P-28ESect-7.7 P-29ESect-7.7 P-30ESect-7.8 P-1CPSect-7.8 P-2CPSect-7.8 P-3CPSect-7.8 P-4CPSect-7.8 P-5CPSect-7.8 P-6CPSect-7.8 P-1SWUSect-7.8 P-2SWUSect-7.8 P-3SWUSect-7.8 P-4SWUSect-7.8 P-5SWUSect-7.8 P-6SWUSect-7.8 P-7SWUSect-7.8 P-8SWUSect-7.8 P-9SWUSect-7.8 P-10SWUSect-7.8 P-11SWUSect-7.8 P-12SWUSect-7.8 P-13SWUSect-7.8 P-14SWUSect-7.8 P-15SWUSect-7.8 P-16SWUSect-7.8 P-1ESect-7.8 P-2ESect-7.8 P-3ESect-7.8 P-4ESect-7.8 P-5ESect-7.8 P-6ESect-7.8 P-7ESect-7.8 P-8ESect-7.8 P-9ESect-7.8 P-10ESect-7.8 P-11ESect-7.8 P-12ESect-7.8 P-13ESect-7.8 P-14ESect-7.8 P-15ESect-7.8 P-16ESect-7.8 P-17ESect-7.8 P-18ESect-7.8 P-19ESect-7.8 P-20ESect-7.8 P-21ESect-7.8 P-22ESect-7.8 P-23ESect-7.8 P-24ESect-7.8 P-25ESect-7.8 P-26ESect-7.8 P-27ESect-7.8 P-28ESect-7.8 P-29ESect-7.8 P-30ESect-7.8 P-31ESect-7.8 P-32ESect-7.8 P-33ESect-7.8 P-34ESect-7.8 P-35ESect-7.8 P-36ESect-7.8 P-37ESect-7.8 P-38ESect-7.8 P-39ESect-7.8 P-40ESect-7.8 P-41ESect-7.8 P-42ESect-7.8 P-43ESect-7.8 P-44ESect-7.8 P-45ESect-7.8 P-46ESect-7.8 P-47ESect-7.8 P-48ESect-7.8 P-49ESect-7.8 P-50ESect-7.8 P-51ESect-7.8 P-52ESect-7.8 P-53ESect-7.8 P-54ESect-7.8 P-55ESect-7.8 P-56ESect-7.8 P-57ESect-7.8 P-58ESect-7.8 P-59ESect-7.8 P-60ESect-7.9 P-1CPSect-7.9 P-2CPSect-7.9 P-3CPSect-7.9 P-4CPSect-7.9 P-5CPSect-7.9 P-1SWUSect-7.9 P-2SWUSect-7.9 P-3SWUSect-7.9 P-4SWUSect-7.9 P-5SWUSect-7.9 P-6SWUSect-7.9 P-7SWUSect-7.9 P-8SWUSect-7.9 P-9SWUSect-7.9 P-10SWUSect-7.9 P-1ESect-7.9 P-2ESect-7.9 P-3ESect-7.9 P-4ESect-7.9 P-5ESect-7.9 P-6ESect-7.9 P-7ESect-7.9 P-8ESect-7.9 P-9ESect-7.9 P-10ESect-7.9 P-11ESect-7.9 P-12ESect-7.9 P-13ESect-7.9 P-14ESect-7.9 P-15ESect-7.9 P-16ESect-7.9 P-17ESect-7.9 P-18ESect-7.9 P-19ESect-7.9 P-20ESect-7.9 P-21ESect-7.9 P-22ESect-7.9 P-23ESect-7.9 P-24ESect-7.9 P-25ESect-7.9 P-26ESect-7.9 P-27ESect-7.9 P-28ESect-7.9 P-29ESect-7.9 P-30ESect-7.9 P-31ESect-7.9 P-32ESect-7.9 P-33ESect-7.9 P-34ESect-7.9 P-35ESect-7.9 P-36ECh-7 P-1RECh-7 P-2RECh-7 P-3RECh-7 P-4RECh-7 P-5RECh-7 P-6RECh-7 P-7RECh-7 P-8RECh-7 P-9RECh-7 P-10RECh-7 P-11RECh-7 P-12RECh-7 P-13RECh-7 P-14RECh-7 P-15RECh-7 P-16RECh-7 P-17RECh-7 P-18RECh-7 P-19RECh-7 P-20RECh-7 P-21RECh-7 P-22RECh-7 P-23RECh-7 P-24RECh-7 P-25RECh-7 P-26RECh-7 P-27RECh-7 P-28RECh-7 P-29RECh-7 P-30RECh-7 P-31RECh-7 P-32RECh-7 P-33RECh-7 P-34RECh-7 P-35RECh-7 P-36RECh-7 P-37RECh-7 P-38RECh-7 P-39RECh-7 P-40RECh-7 P-41RECh-7 P-42RECh-7 P-43RECh-7 P-44RECh-7 P-45RECh-7 P-46RECh-7 P-47RECh-7 P-48RECh-7 P-49RECh-7 P-50RECh-7 P-51RECh-7 P-52RECh-7 P-53RECh-7 P-54RECh-7 P-55RECh-7 P-56RECh-7 P-57RECh-7 P-58RECh-7 P-59RECh-7 P-60RECh-7 P-61RECh-7 P-62RECh-7 P-63RECh-7 P-64RECh-7 P-65RECh-7 P-66RECh-7 P-67RECh-7 P-68RECh-7 P-69RECh-7 P-70RECh-7 P-71RECh-7 P-72RECh-7 P-73RECh-7 P-74RECh-7 P-75RECh-7 P-76RECh-7 P-77RECh-7 P-78RECh-7 P-79RECh-7 P-80RECh-7 P-81RECh-7 P-82RECh-7 P-83RECh-7 P-84RECh-7 P-85RECh-7 P-86RECh-7 P-87RECh-7 P-88RECh-7 P-89RECh-7 P-90RECh-7 P-91RECh-7 P-92RECh-7 P-93RECh-7 P-94RECh-7 P-95RECh-7 P-96RECh-7 P-97RECh-7 P-98RECh-7 P-99RECh-7 P-100RECh-7 P-101RECh-7 P-102RECh-7 P-103RECh-7 P-104RECh-7 P-1TYSCh-7 P-2TYSCh-7 P-3TYSCh-7 P-4TYSCh-7 P-5TYSCh-7 P-6TYSCh-7 P-7TYSCh-7 P-8TYSCh-7 P-9TYSCh-7 P-10TYSCh-7 P-11TYSCh-7 P-12TYSCh-7 P-13TYSCh-7 P-14TYSCh-7 P-15TYSCh-7 P-16TYSCh-7 P-17TYSCh-7 P-18TYSCh-7 P-19TYSCh-7 P-20TYSCh-7 P-21TYSCh-7 P-22TYS

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Differentiate the function. k(r) = er + re

Calculus: Early Transcendentals

In Exercises 1728, use the logarithm identities to obtain the missing quantity.

Finite Mathematics and Applied Calculus (MindTap Course List)

Solving Equations Find all real solutions of the equation. 60. x2 + 24x + 144 = 0

Precalculus: Mathematics for Calculus (Standalone Book)

In Exercises 35-38, find an equation of the line that has slope m and y-intercept b. 35. m = 3; b = 4

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

In problems 27-30, find. 30.

Mathematical Applications for the Management, Life, and Social Sciences

Classify each angle as right, acute, or obtuse:

Elementary Technical Mathematics

In Exercises 116, determine whether the argument is valid. pqqr~p~p~r

Finite Mathematics for the Managerial, Life, and Social Sciences

The equation of the line through (4, 10, 8) and (3, 5, 1) is:

Study Guide for Stewart's Multivariable Calculus, 8th

True or False: In general, better approximations to the area under the curve y = f(x) between x = a and x = b a...

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Describe the relationship between the alpha level and the likelihood of making a Type I error.

Research Methods for the Behavioral Sciences (MindTap Course List)