   Chapter 15.1, Problem 10E

Chapter
Section
Textbook Problem

Evaluate the double integral by first identifying it as the volume of a solid.10. ∬ R ( 2 x + 1 ) d A ,   R = { ( x , y ) | 0 ≤ x ≤ 2 , 0 ≤ y ≤ 4 }

To determine

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

Explanation

Given:

The function is f(x,y)=2x+1 .

The rectangular region, R={(x,y)|0x2,0y4} .

Interpretation:

From the given f(x,y) and R, it is observed that the surface is a rectangular solid by surmounted by a triangular cylinder.

Calculation:

Since x is positive and f(x,y)=2x+1 is greater than 0, it is enough to find the value of double integral in order to find the volume of the solid.

R(2x+1)dA=02[04(2x+1)dy]dx=02

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

Describe the set of points (x,y) such that x2+y2=0.

Finite Mathematics and Applied Calculus (MindTap Course List)

Sketch the graph of the line that passes through the point (3, 2) and has slope 23.

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

The graph of θ = 2 in polar coordinates is a: circle line spiral 3-leaved rose

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