   Chapter 15.1, Problem 34E

Chapter
Section
Textbook Problem

Calculate the double integral.34. ∬ R 1 1 + x + y d A ,   R = [ 1 , 3 ] × [ 1 , 2 ]

To determine

To calculate: The value of given double integral over the region R.

Explanation

Given

The rectangular region is, R=[1,3]×[1,2] .

Calculation:

Compute the value of double integration as follows.

R11+x+ydA=13[1211+x+ydy]dx=13[ln(1+x+y)]12dx=13[ln(x+3)ln(x+2)]dx=13ln(x+3)dx13ln(x+2)dx

Apply the technique of integration by parts,

Let u1=ln(3+x) and dv1=dx .

Then, v1=x .

Let u2=ln(2+x) and dv2=dy .

Then, v2=y .

The value of the given double integral becomes,

Rx1+x+ydA=[xln(3+x)]1313x.13+xdx[xln(2+x)]13+13x.12+xdx=[xln(3+x)]13133+x33+xdx[xln(2+x)]13+132+x22+xdx=[xln(3+x)]1313dx+31313+xdx[xln(2+x)]13+13dx21312+x

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

In Exercises 7-12, solve for y in terms of x. x=2y14

Calculus: An Applied Approach (MindTap Course List)

Find the limit or show that it does not exist. limxx+3x24x1

Single Variable Calculus: Early Transcendentals, Volume I

Evaluate the expression sin Exercises 116. (2)3

Finite Mathematics and Applied Calculus (MindTap Course List)

Solve for y in terms of x: 4x5y=10

Elementary Technical Mathematics

y-intercept 6, parallel to the line 2x + 3y + 4 = 0

Single Variable Calculus: Early Transcendentals

It does not exist.

Study Guide for Stewart's Multivariable Calculus, 8th 