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

Explain why the double integral ΩdAgives the area of the regionΩ . Illustrate your explanation with an example.

Short Answer

Expert verified

It is solved by solving type I integral.

Step by step solution

01

Given Information

We are given double integral ΩdAover region Ω

02

Simplification

Consider arbitrary type I region bounded on left by x=a, to right by x=b

below by y=g1(x)and above by y=g2(x)

Integral ΩdAover type I is calculated by taking elementary area of width xwith one end lying over y=g1(x)and other over y=g2(x)

The integral becomes

ΩdA=abg1(x)g2(x)dydx

ΩdA=ab[y]g1(x)g2(x)dx

=abg2(x)-g1(x)dx

Hence, integralΩdAgives area over regionΩ

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