   Chapter 7.9, Problem 1E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

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

# Finding the Volume of a Solid Region In Exercises 1-6, find the volume of the solid region bounded in the first octant by the plane. See Example 1. z = 5 − x − y

To determine

To calculate: The volume of solid region bounded in first octane and the plane z=5xy.

Explanation

Given information:

The provided equation of plane is z=5xy.

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 plane,

z=5xy

The following table shown different coordinate of (x,y,z) for z=5xy.

 x-Coordinate y-Coordinate z-Coordinate (x,y,z) Coordinate 0 0 5 (0,0,5) 0 5 0 (0,5,0) 5 0 0 (5,0,0)

The graph of function z=5xy in first octant shown below.

Substitute, 0 for z in equation of plane z=5xy.

5xy=0x+y=5

The region R is bounded by the line x=0,y=0 and y=5x.

The following table shown different coordinate of (x,y) for x+y=5.

 x-Coordinate y-Coordinate (x,y) Coordinate 0 5 (5,0) 5 0 (0,5)

The sketch of region R: x+y=5 in the xy-plane.

One way to set up the double integration is to choose x as the outer variable with that choice. The bounds for x are 0x5 and bounds for y are 0y5x and another choose to set up the double integration is to choose y as the outer variable. with that choice, The bounds for y are 0y5 and bounds for x are 0x5y

### 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 516, evaluate the given quantity. log1/212

Finite Mathematics and Applied Calculus (MindTap Course List)

#### converges to: 2 the series diverges

Study Guide for Stewart's Multivariable Calculus, 8th

#### True or False: n=1an converges if and only if limnan=0.

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