A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
a. find the area enclosed in the inner loop of the limacon, r=1+2costheta.
b. find hte area inside the limacon but outside the inner loop
 2 years ago
a. find the area enclosed in the inner loop of the limacon, r=1+2costheta. b. find hte area inside the limacon but outside the inner loop

This Question is Closed

eliassaab
 2 years ago
Best ResponseYou've already chosen the best response.0b) \[2 \int_0^{\frac{2 \pi }{3}} \frac{1}{2} (2 \cos (\theta )+1)^2 \, d\theta=\frac{3 \sqrt{3}}{2}+2 \pi \]

eliassaab
 2 years ago
Best ResponseYou've already chosen the best response.0a)\[2 \int_{\frac{2 \pi }{3}}^{\pi } \frac{1}{2} (2 \cos (\theta )+1)^2 \, d\theta=\pi \frac{3 \sqrt{3}}{2} \]

itzmashy
 2 years ago
Best ResponseYou've already chosen the best response.0i'm not supposed to use a double integral?

colorful
 2 years ago
Best ResponseYou've already chosen the best response.1the way I see it the first step is to find the bounds on theta I think having the picture ion front of you helps

eliassaab
 2 years ago
Best ResponseYou've already chosen the best response.0Both of them are single integrals

colorful
 2 years ago
Best ResponseYou've already chosen the best response.1http://www.wolframalpha.com/input/?i=plot%20r%3D1%2B2costheta.%20%20&t=crmtb01

colorful
 2 years ago
Best ResponseYou've already chosen the best response.1sorry those bounds are wrong \[r=0=1+2\cos\theta\implies \theta=\frac{2\pi}3,\frac{4\pi}3\]which means the bounds on theta are\[\frac{2\pi}3\le\theta\le\frac{4\pi}3\]

colorful
 2 years ago
Best ResponseYou've already chosen the best response.1The bounds on r are just the polar function itself\[0\le r\le1+2\cos\theta\]and the area differential in polar coordinates is\[dA=rdrd\theta\]hence the intergal for the area of the inner loop should be\[\large \int\int dA=\int_{\frac{2\pi}3}^{\frac{4\pi}3}\int_{0}^{1+2r\cos\theta}rdr\theta\]

colorful
 2 years ago
Best ResponseYou've already chosen the best response.1...I assumed we are working in the interval \([0,2\pi]\)

itzmashy
 2 years ago
Best ResponseYou've already chosen the best response.0and @colorful i'm at work so i can't be checking this all the time :( but it was a homework problem last night and it blew my mind cuz i've never even seen a limacon before last night.. _"

eliassaab
 2 years ago
Best ResponseYou've already chosen the best response.0The bounds for my solutions above are fine
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.