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

Let ρ(x,y,z)be a density function defined on the tetrahedron Ωwith vertices (0,0,0),(2,0,0),(0,4,0),and (0,0,3). Set up iterated integrals representing the mass of , using all six distinct orders of integration.

Short Answer

Expert verified

The five distinct orders of integration representing the mass of Ωare,

role="math" localid="1650366865545" 0103-3x204-2x-4y3ρx,y,zdydzdx0302-2x304-2x-4y3ρx,y,zdydxdz0403-3y402-y2-2z3ρx,y,zdxdzdy0304-4z302-y2-2z3ρx,y,zdxdydz0402-y203-3x2-3y4ρx,y,zdzdxdy

Step by step solution

01

Step 1. Given information

Let ρ(x,y,z)be a density function defined on the tetrahedronΩwith vertices localid="1650434213243" (0,0,0),(2,0,0),(0,4,0),and localid="1650434285733" (0,0,3).

02

Step 2. The other five mass integrals are,

0402-y203-3x2-3y4ρx,y,zdzdxdy.

Since taking zand xafter ythelimits from oblique plane becomes,

0y4,0x2-y2and0z1-3x2-3y4.
03

Step 3. Similarly the other four mass integrals are,

0103-3x204-2x-4y3ρx,y,zdydzdx0302-2x304-2x-4y3ρx,y,zdydxdz0403-3y402-y2-2z3ρx,y,zdxdzdy0304-4z302-y2-2z3ρx,y,zdxdydz

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

Study anywhere. Anytime. Across all devices.

Sign-up for free