/*! 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. 25 If the density at each point in ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Q. 25 (page 991)

If the density at each point in T is proportional to the point's distance from the y-axis, find the mass ofT.

Short Answer

Expert verified

The mass of the triangular lamina is

m=23k

Step by step solution

01

Given information

The objective of this problem is to find the mass of the triangular region.

02

calculation

For an example, take a triangle with vertices (0,0),(1,1) and (1,-1).

Mass of the lamina is can be calculated by the formula

m=鈭�惟蚁(x,y)dA

蚁(x,y)is the uniform density of the lamina. If蚁(x,y)is proportional to the point's distance from the y - axis.

蚁(x,y)=kxm=鈭�01鈭�-xxkxdydx

Integrate with respect to y first.

m=鈭�01kx[y]-xxdxm=鈭�01kx[x-(-x)]dxm=2k鈭�01x2dx

Integrate with respect to x.

m=2kx3301

Substitute the limits

m=23k

Thus, the mass of the triangular lamina is

m=23k

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

Evaluate the iterated integral :

鈭�13鈥�鈭�鈭�15鈥�鈭�03鈥�xy2zdzdydx

Evaluate the triple integrals over the specified rectangular solid region.

鈭�R鈥�zsin鈦�xcos鈦�ydV,whereR=(x,y,z)鈭�0鈮�x鈮�蟺,3蟺2鈮�y鈮�2蟺,and1鈮�z鈮�3

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

鈭�鈭�RxsinxcosydA,whereR={(x,y)|鈭�3鈮�x鈮�2and鈭�2鈮�y鈮�2}

Earlier in this section, we showed that we could use Fubini鈥檚 theorem to evaluate the integral 鈭�鈭�Rx2ydAand we showed that 鈭�25鈭�13x2ydxdy=91Now evaluate the double integral by evaluating the iterated integral鈭�13鈭�25x2ydydx.

Use the lamina from Exercise 64, but assume that the density is proportional to the distance from the x-axis.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

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.