Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 13: Q 5. (page 1014)

Which of the iterated integrals in Exercises below could correctly

be used to evaluate the double integral:

∫14∫26f(x,y)dydx

Short Answer

Expert verified

The iterated integral will give correct value of ∬Rf(x,y)dA

Step by step solution

01

Given Information

Rectangular region is bounded by linesx=1,x=4,y=2andy=6

02

Definition of integral region

Consider an iterated integral

∫14∫26f(x,y)dydx

The region is rectangular with is sides parallel to xyplane.

It can be of either type.

For type I , the integration is first done with respect to yand then x.

The inner integral to be solved wrty.

03

Simplification

In ∫14∫26f(x,y)dydx, inner integral is solved wrt yand integral is solved wrt x

Hence, he iterated integral will give correct value of ∬Rf(x,y)dA

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

In the following lamina, all angles are right angles and the density is constant:

Evaluate the iterated integral :

∫0π/2 ∫0cos⁡y ∫0sin⁡y (2x+y)dzdxdy

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

Exercise 41 with the order dy dx dz.

Evaluate each of the double integrals in Exercises 37–54 as iterated integrals.

∫∫RxsinxcosydA,whereR={(x,y)|−3≤x≤2and−2≤y≤2}

In Exercises 61–64, let R be the rectangular solid defined by

R=(x,y,z)|0≤a1≤x≤a2,0≤b1≤y≤b2,0≤c2≤z≤c2.

Assume that the density of R is uniform throughout.

(a) Without using calculus, explain why the center of

mass is a1+a22,b1+b22,c1+c22.

(b) Verify that a1+a22,b1+b22,c1+c22is the center of mass by using the appropriate integral expressions.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

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.

Sign-up for free