BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

Solutions

Chapter
Section
BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Evaluate the iterated integral.

6. 0 1 0 1 0 1 z 2 z y + 1 d x d z d y

To determine

To evaluate: The iterated integral.

Explanation

Given:

The function is f(x,y,z)=zy+1 .

The region is B={(x,y,z)|0x1z2,0y1,0z1} .

Formula used:

If g(x) is the function of x and h(y) is the function of y then,

abcdg(x)h(y)dydx=abg(x)dxcdh(y)dy (1)

Calculation:

The given integral is, 010101z2zy+1dxdzdy .

Integrate the given integral with respect to x and apply the limit of it.

010101z2zy+1dxdzdy=0101[zy+1x]01z2dzdy=0101[(zy+11z2)(zy+1(0))]dzdy=0101[z1z2y+1]dzdy

By the equation (1), 010101z2zy+1dxdzdy=011y+1dy01[z1z2]dz (2)

By substitution method, let u=z2 .

Then, the derivative of u is du=2dz .

Thus, there is a change in the limit values of the integration such as,

If z=0 , then u=0 and if z=1 , then u=1

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

Chapter 15 Solutions

Show all chapter solutions add
Sect-15.1 P-11ESect-15.1 P-12ESect-15.1 P-13ESect-15.1 P-14ESect-15.1 P-15ESect-15.1 P-16ESect-15.1 P-17ESect-15.1 P-18ESect-15.1 P-19ESect-15.1 P-20ESect-15.1 P-21ESect-15.1 P-22ESect-15.1 P-23ESect-15.1 P-24ESect-15.1 P-25ESect-15.1 P-26ESect-15.1 P-27ESect-15.1 P-28ESect-15.1 P-29ESect-15.1 P-30ESect-15.1 P-31ESect-15.1 P-32ESect-15.1 P-33ESect-15.1 P-34ESect-15.1 P-35ESect-15.1 P-36ESect-15.1 P-37ESect-15.1 P-38ESect-15.1 P-39ESect-15.1 P-40ESect-15.1 P-41ESect-15.1 P-42ESect-15.1 P-43ESect-15.1 P-44ESect-15.1 P-47ESect-15.1 P-48ESect-15.1 P-49ESect-15.1 P-50ESect-15.1 P-52ESect-15.2 P-1ESect-15.2 P-2ESect-15.2 P-3ESect-15.2 P-4ESect-15.2 P-5ESect-15.2 P-6ESect-15.2 P-7ESect-15.2 P-8ESect-15.2 P-9ESect-15.2 P-10ESect-15.2 P-11ESect-15.2 P-12ESect-15.2 P-13ESect-15.2 P-14ESect-15.2 P-15ESect-15.2 P-16ESect-15.2 P-17ESect-15.2 P-18ESect-15.2 P-19ESect-15.2 P-20ESect-15.2 P-21ESect-15.2 P-22ESect-15.2 P-23ESect-15.2 P-24ESect-15.2 P-25ESect-15.2 P-26ESect-15.2 P-27ESect-15.2 P-28ESect-15.2 P-29ESect-15.2 P-30ESect-15.2 P-31ESect-15.2 P-32ESect-15.2 P-33ESect-15.2 P-34ESect-15.2 P-35ESect-15.2 P-36ESect-15.2 P-37ESect-15.2 P-38ESect-15.2 P-39ESect-15.2 P-40ESect-15.2 P-45ESect-15.2 P-46ESect-15.2 P-47ESect-15.2 P-48ESect-15.2 P-49ESect-15.2 P-50ESect-15.2 P-51ESect-15.2 P-52ESect-15.2 P-53ESect-15.2 P-54ESect-15.2 P-55ESect-15.2 P-56ESect-15.2 P-57ESect-15.2 P-58ESect-15.2 P-59ESect-15.2 P-60ESect-15.2 P-61ESect-15.2 P-62ESect-15.2 P-63ESect-15.2 P-64ESect-15.2 P-65ESect-15.2 P-66ESect-15.2 P-67ESect-15.2 P-68ESect-15.2 P-69ESect-15.3 P-1ESect-15.3 P-2ESect-15.3 P-3ESect-15.3 P-4ESect-15.3 P-5ESect-15.3 P-6ESect-15.3 P-7ESect-15.3 P-8ESect-15.3 P-9ESect-15.3 P-10ESect-15.3 P-11ESect-15.3 P-12ESect-15.3 P-13ESect-15.3 P-14ESect-15.3 P-15ESect-15.3 P-16ESect-15.3 P-17ESect-15.3 P-18ESect-15.3 P-19ESect-15.3 P-20ESect-15.3 P-21ESect-15.3 P-22ESect-15.3 P-23ESect-15.3 P-24ESect-15.3 P-25ESect-15.3 P-26ESect-15.3 P-27ESect-15.3 P-28ESect-15.3 P-29ESect-15.3 P-30ESect-15.3 P-31ESect-15.3 P-32ESect-15.3 P-33ESect-15.3 P-34ESect-15.3 P-35ESect-15.3 P-36ESect-15.3 P-37ESect-15.3 P-38ESect-15.3 P-39ESect-15.3 P-40ESect-15.3 P-41ESect-15.4 P-1ESect-15.4 P-2ESect-15.4 P-3ESect-15.4 P-4ESect-15.4 P-5ESect-15.4 P-6ESect-15.4 P-7ESect-15.4 P-8ESect-15.4 P-9ESect-15.4 P-10ESect-15.4 P-11ESect-15.4 P-12ESect-15.4 P-13ESect-15.4 P-14ESect-15.4 P-15ESect-15.4 P-16ESect-15.4 P-17ESect-15.4 P-18ESect-15.4 P-19ESect-15.4 P-20ESect-15.4 P-21ESect-15.4 P-22ESect-15.4 P-23ESect-15.4 P-24ESect-15.4 P-27ESect-15.4 P-28ESect-15.4 P-29ESect-15.4 P-30ESect-15.4 P-32ESect-15.4 P-33ESect-15.5 P-1ESect-15.5 P-2ESect-15.5 P-3ESect-15.5 P-4ESect-15.5 P-5ESect-15.5 P-6ESect-15.5 P-7ESect-15.5 P-8ESect-15.5 P-9ESect-15.5 P-10ESect-15.5 P-11ESect-15.5 P-12ESect-15.5 P-13ESect-15.5 P-14ESect-15.5 P-21ESect-15.5 P-22ESect-15.5 P-23ESect-15.5 P-24ESect-15.6 P-1ESect-15.6 P-2ESect-15.6 P-3ESect-15.6 P-4ESect-15.6 P-5ESect-15.6 P-6ESect-15.6 P-7ESect-15.6 P-8ESect-15.6 P-9ESect-15.6 P-10ESect-15.6 P-11ESect-15.6 P-12ESect-15.6 P-13ESect-15.6 P-14ESect-15.6 P-15ESect-15.6 P-16ESect-15.6 P-17ESect-15.6 P-18ESect-15.6 P-19ESect-15.6 P-20ESect-15.6 P-21ESect-15.6 P-22ESect-15.6 P-25ESect-15.6 P-26ESect-15.6 P-27ESect-15.6 P-28ESect-15.6 P-29ESect-15.6 P-30ESect-15.6 P-31ESect-15.6 P-32ESect-15.6 P-33ESect-15.6 P-34ESect-15.6 P-35ESect-15.6 P-36ESect-15.6 P-37ESect-15.6 P-38ESect-15.6 P-39ESect-15.6 P-40ESect-15.6 P-41ESect-15.6 P-42ESect-15.6 P-43ESect-15.6 P-44ESect-15.6 P-45ESect-15.6 P-46ESect-15.6 P-47ESect-15.6 P-48ESect-15.6 P-51ESect-15.6 P-52ESect-15.6 P-53ESect-15.6 P-54ESect-15.7 P-1ESect-15.7 P-2ESect-15.7 P-3ESect-15.7 P-4ESect-15.7 P-5ESect-15.7 P-6ESect-15.7 P-7ESect-15.7 P-8ESect-15.7 P-9ESect-15.7 P-10ESect-15.7 P-11ESect-15.7 P-12ESect-15.7 P-13ESect-15.7 P-14ESect-15.7 P-15ESect-15.7 P-16ESect-15.7 P-17ESect-15.7 P-18ESect-15.7 P-19ESect-15.7 P-20ESect-15.7 P-21ESect-15.7 P-22ESect-15.7 P-23ESect-15.7 P-24ESect-15.7 P-25ESect-15.7 P-26ESect-15.7 P-27ESect-15.7 P-28ESect-15.7 P-29ESect-15.7 P-30ESect-15.7 P-31ESect-15.8 P-1ESect-15.8 P-2ESect-15.8 P-3ESect-15.8 P-4ESect-15.8 P-5ESect-15.8 P-6ESect-15.8 P-7ESect-15.8 P-8ESect-15.8 P-9ESect-15.8 P-10ESect-15.8 P-11ESect-15.8 P-12ESect-15.8 P-13ESect-15.8 P-14ESect-15.8 P-15ESect-15.8 P-16ESect-15.8 P-17ESect-15.8 P-18ESect-15.8 P-19ESect-15.8 P-20ESect-15.8 P-21ESect-15.8 P-22ESect-15.8 P-23ESect-15.8 P-24ESect-15.8 P-25ESect-15.8 P-26ESect-15.8 P-27ESect-15.8 P-28ESect-15.8 P-29ESect-15.8 P-30ESect-15.8 P-31ESect-15.8 P-32ESect-15.8 P-33ESect-15.8 P-34ESect-15.8 P-35ESect-15.8 P-36ESect-15.8 P-37ESect-15.8 P-38ESect-15.8 P-41ESect-15.8 P-42ESect-15.8 P-43ESect-15.8 P-44ESect-15.8 P-45ESect-15.8 P-46ESect-15.8 P-48ESect-15.8 P-49ESect-15.9 P-1ESect-15.9 P-2ESect-15.9 P-3ESect-15.9 P-4ESect-15.9 P-5ESect-15.9 P-6ESect-15.9 P-7ESect-15.9 P-8ESect-15.9 P-9ESect-15.9 P-10ESect-15.9 P-11ESect-15.9 P-12ESect-15.9 P-13ESect-15.9 P-14ESect-15.9 P-15ESect-15.9 P-16ESect-15.9 P-17ESect-15.9 P-18ESect-15.9 P-19ESect-15.9 P-20ESect-15.9 P-21ESect-15.9 P-22ESect-15.9 P-23ESect-15.9 P-24ESect-15.9 P-25ESect-15.9 P-26ESect-15.9 P-27ESect-15.9 P-28ECh-15 P-1RCCCh-15 P-2RCCCh-15 P-3RCCCh-15 P-4RCCCh-15 P-5RCCCh-15 P-6RCCCh-15 P-7RCCCh-15 P-8RCCCh-15 P-9RCCCh-15 P-10RCCCh-15 P-1RQCh-15 P-2RQCh-15 P-3RQCh-15 P-4RQCh-15 P-5RQCh-15 P-6RQCh-15 P-7RQCh-15 P-8RQCh-15 P-9RQCh-15 P-1RECh-15 P-2RECh-15 P-3RECh-15 P-4RECh-15 P-5RECh-15 P-6RECh-15 P-7RECh-15 P-8RECh-15 P-9RECh-15 P-10RECh-15 P-11RECh-15 P-12RECh-15 P-13RECh-15 P-14RECh-15 P-15RECh-15 P-16RECh-15 P-17RECh-15 P-18RECh-15 P-19RECh-15 P-20RECh-15 P-21RECh-15 P-22RECh-15 P-23RECh-15 P-24RECh-15 P-25RECh-15 P-26RECh-15 P-27RECh-15 P-28RECh-15 P-29RECh-15 P-30RECh-15 P-31RECh-15 P-32RECh-15 P-33RECh-15 P-34RECh-15 P-35RECh-15 P-36RECh-15 P-37RECh-15 P-38RECh-15 P-39RECh-15 P-40RECh-15 P-41RECh-15 P-42RECh-15 P-43RECh-15 P-44RECh-15 P-45RECh-15 P-47RECh-15 P-48RECh-15 P-49RECh-15 P-51RECh-15 P-52RECh-15 P-53RECh-15 P-54RECh-15 P-55RECh-15 P-56RECh-15 P-57RECh-15 P-58RECh-15 P-59RECh-15 P-60RECh-15 P-1PCh-15 P-2PCh-15 P-3PCh-15 P-4PCh-15 P-5PCh-15 P-6PCh-15 P-7PCh-15 P-8PCh-15 P-9PCh-15 P-10PCh-15 P-11PCh-15 P-12PCh-15 P-13P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

In Exercises 5-8, solve for x. 3x2x224x=0

Calculus: An Applied Approach (MindTap Course List)

In Exercises 516, evaluate the given quantity. log1/212

Finite Mathematics and Applied Calculus (MindTap Course List)

Finding a Limit In Exercises 11-28, find the limit. limx6x2

Calculus: Early Transcendental Functions

Use the definition of the derivative to find the slope of the tangent line to the graph of the function f(x) = ...

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

Find the derivatives of the functions in Problems 1-10. 5.

Mathematical Applications for the Management, Life, and Social Sciences

Solve the differential equation. 14. tlntdrdt+r=tet

Single Variable Calculus: Early Transcendentals

Prove each identity. sec(A+B)=cos(AB)cos2Asin2B

Trigonometry (MindTap Course List)

The angle θ at the right has cosine:

Study Guide for Stewart's Multivariable Calculus, 8th

A mosquito population of 100 grows to 500 after two weeks. If the population follows an exponential growth mode...

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