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

Calculate the surface area of the solid of revolution obtained by revolving the region between fx=2x3and the x-axis on 0,3around the x-axis.

Short Answer

Expert verified

The surface area of the solid of revolution obtained by revolving the region between fx=2x3and the x-axis on 0,3around the x-axis is, 1526.81(approximately) square units.

Step by step solution

01

Step 1. Given information

The region betweenfx=2x3and the x-axis on0,3.

02

Step 2. The formula for the surface area is,

Surface area=2πabfx1+f'x2dx.

Let fx=2x3,f'x=6x2.

Substitute the known values in the formula.

Surface area=2π032x31+6x22dx

role="math" localid="1648890749974" =2π032x31+36x4dx

Let u=1+36x4,du=144x3.

role="math" localid="1648892010258" 2πx=0x=32x31+36x4dx=2π2144x=0x=3udu=π3623u3203=π36231+36x43203=π541+36x603=π541+3636-1+3606=π541+26,244-1=486π1526.81

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