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

Each of the integrals or integral expressions in Exercise represents the area of a region in the plane. Use polar coordinates to sketch the region and evaluate the expressions.

20π/20sin3θrdrdθ

Short Answer

Expert verified

The integral's value is20π/20sin3θrdrdθ=π4

Step by step solution

01

given information 

Let consider the given integral is20π/20sin3θrdrdθ

02

Finding establish the expression

The goal of this issue is to sketch the region and assess the expression using polar coordinates 20π/20sin3θrdrdθ

Using, r=0,r=sinθandθ=0,θ=π/2

θ
r=sin3θ
00
π/6
1.0
π/4
0.7071
π/3
0
π/2
-1.0
03

Calculations 

20π/20sin3θrdrdθ=20π/2r220sin3θ=20π/2sin23θ02θ=20π/2(1cos6θ)4

Integrate in relation to θ,

20π/20sin3θrdrdθ=2{θ(sin6θ6}40π/2cosxdx=sinx

Pointing the limits,

20π/20sin3θrdrdθ=2{π/2(sin3π)60}4=π4

As a result, the integral value is20π/20sin3θrdrdθ=π4

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