/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 36 Describe the three-dimensional r... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Q. 36 (page 1055)

Describe the three-dimensional region expressed in each iterated integral in Exercises 35鈥44.

鈭-15鈭-32鈭48f(x,y,z)dzdxdy

Short Answer

Expert verified

The three-dimensional region is,

鈩={(x,y,z)鈭-3鈮x鈮2,-1鈮y鈮5,4鈮z鈮8}

Step by step solution

01

Step 1. Given Information

We are given,

鈭-15鈭-32鈭48f(x,y,z)dzdxdy

02

Step 2. The three dimensional region.

By the definition of triple integral 鈭a1a1鈭b1b2鈭c1c2f(x,y,z)dzdydxrepresent the volume of the solid region鈩=(x,y,z)鈭a1鈮x鈮a2,b1鈮y鈮b2,c1鈮z鈮c2

Using this definition,

The given iterated triple integral 鈭-15鈭-32鈭48f(x,y,z)dzdxdyrepresents the volume of the rectangular solid given by鈩={(x,y,z)鈭-3鈮x鈮2,-1鈮y鈮5,4鈮z鈮8}

Since by taking the order of the integration in the given iterated integral order that is dzdxdy.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Explain how to construct a midpoint Riemann sum for a function of two variables over a rectangular region for which each (xj*,yk*) is the midpoint of the subrectangle

Rjk={(x,y)鈭xj-1鈮xj*鈮xjandyk-1鈮yk*鈮yk}.

Refer to your answer to Exercise 10 or to Definition 13.3.

Describe the three-dimensional region expressed in each iterated integral in Exercises 35鈥44.

鈭-33鈭-9-x29-x2鈭-9-x2-y29-x2-y2f(x,y,z)dzdydx

Evaluate the iterated integral :

鈭01鈥鈭03鈥鈭0sin鈭1鈦x鈥(x+y)dzdydx

Evaluate the triple integrals over the specified rectangular solid region.

鈭R鈥(x+2y+3z)dV, whereR={(x,y,z)鈭0鈮x鈮4,1鈮y鈮5,and2鈮z鈮7}

In Exercises 45鈥52, rewrite the indicated integral with the specified order of integration.

Exercise 42 with the order dy dx dz.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.