Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

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=Ωρ(x,y)dA

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

ρ(x,y)=kxm=01-xxkxdydx

Integrate with respect to y first.

m=01kx[y]-xxdxm=01kx[x-(-x)]dxm=2k01x2dx

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 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

See all solutions

Recommended explanations on Math Textbooks

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