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 a<band c<dbe real numbers, and let Rbe the

rectangle in the xy-plane defined by

R={(x,y)axbandcyd}.

Prove that role="math" localid="1653851117688" RdA=(b-a)(d-c), what is the relation between Rand product of(b-a)(d-c)?

Short Answer

Expert verified

This is evaluated using Fubini's theoremRdA=abcddydx

Step by step solution

01

Given Information

It is given that a<bandc<d, a,b,c,dare real numbers.

R is rectangle in cartesian plane defined byR={(x,y)axbandcyd}

02

Use Fubini's Theorem

By theorem RdA=abcddydx

Treat xas constant

=abcddydx

=ab[y]y=cy=ddx

=(d-c)abdx

=(d-c)[x]x=ax=b

=(d-c)(b-a)

RdA=(d-c)(b-a)

Hence proved.

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