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

Reversing the order of integration: Sketch the region determined by the limits of the given iterated integrals, and then evaluate the integrals by reversing the order of integration.

09y311+x3dxdy

Short Answer

Expert verified

0x20311+x3dxdy=13ln28

Step by step solution

01

Draw the region

The region determined by the limits of the given iterated integral is shown below,

02

Reversing the order of integration  

From the above diagram, reversing the order of integration.

09y311+x3dxdy0x20311+x3dxdy

03

Evaluate the integral

I=0x20311+x3dxdyI=0x2dy0311+x3dxI=03x21+x3dx

Substitute,

1+x3=t3x2dx=dtdx=13x2dtWhenx=0,t=1+0=1Whenx=3,t=1+33=28

Therefore,

I=131281tdtI=13lnt128I=13ln28

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