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

Evaluate the double integral over the specified region.

Ωx2y3dAwhere Ω is region in first quadrant bounded by curvesy=x2andx=y2

Short Answer

Expert verified

The integral is3110.

Step by step solution

01

Given Information

We are given with Ωx2y3dA

The curves arey=x2andx=y2.

02

Graph

The region in graph is shown below:

03

Simplification

The region of integration is region between y=x2andy=x.

For type I integral

0x1,x2yx

Hence, integral is simplified as

01x2xx2y3dydx=01y44x2xx2dx

=1401x2-x8x2dx

=1401x4-x10dx

=14x55-x111101

=1415-111

=3110

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