Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
itzmashy
Group Title
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
 2 years ago
itzmashy Group Title
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
 2 years ago

This Question is Closed

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

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

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

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

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

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

colorful Group TitleBest ResponseYou've already chosen the best response.1
sorry 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\[\frac{2\pi}3\le\theta\le\frac{4\pi}3\]
 2 years ago

colorful Group TitleBest ResponseYou've already chosen the best response.1
The 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\[\large \int\int dA=\int_{\frac{2\pi}3}^{\frac{4\pi}3}\int_{0}^{1+2r\cos\theta}rdr\theta\]
 2 years ago

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

itzmashy Group TitleBest ResponseYou've already chosen the best response.0
and @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.. _"
 2 years ago

eliassaab Group TitleBest ResponseYou've already chosen the best response.0
The bounds for my solutions above are fine
 2 years ago
See more questions >>>
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.