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

Use Theorem 9.14 to show that the circumference of the circle defined by the polar equation r=ais 2πa.

Short Answer

Expert verified

The length of the curve is2πa.

Step by step solution

01

Step 1. Given Information

The function that bounds the circle isr=a.

02

Step 2. Use the formula of arc length of a polar curve

  • The region is bounded by the curve r=a.
  • The region is a circle, so the boundary arcs will be θ=0toθ=2π.
  • So, the length of the curve will be calculated as follows:

02π(r')2+r2dθ=02π0+a2dθ=a02πdθ=a×2π=2πa

  • Hence, the circumference of the curve is 2πa.

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