Community

Visit the AoPS Book Store.
Login Register Memberlist Search AoPS Blogs Contests Galleries Forum Index
The time now is Mon Dec 07, 2009 1:24 am
All times are UTC - 8
 		View posts since last visit
View unanswered posts
Home » College Playground » Calculus - Real Analysis » Calculus Computations and Tutorials
 
Polar equation
Moderators: College Playground Moderators
Post new topic   Reply to topic View previous topicView next topic
3 Posts • Page 1 of 1
Author Message
ThetaPi
Riemann Hypothesis
Riemann Hypothesis


Offline
Joined: 05 May 2008
Posts: 261
Singapore
To rate posts you must be logged in
#1
Polar equation
Show that the curve whose polar equation is r = a + b \sec \theta, where a > b > 0, has a loop. Prove that the area enclosed by the loop is
a^2 \arccos \frac {b}{a} + b\sqrt{a^2 - b^2} - 2ab \ln \frac {a + \sqrt {a^2 - b^2}}{b}.

PostPosted: Fri Oct 30, 2009 11:12 pm  Back to top 
  ProfilePM
ThetaPi
Riemann Hypothesis
Riemann Hypothesis


Offline
Joined: 05 May 2008
Posts: 261
Singapore
To rate posts you must be logged in
#2
Hello, any one wants to give this problem a try?

PostPosted: Sat Oct 31, 2009 6:04 am  Back to top 
  ProfilePM
Dr Sonnhard Graubner
Birch & Swinnerton Dyer
Birch & Swinnerton Dyer

Offline
Joined: 25 Jul 2004
Posts: 2820
Germany
To rate posts you must be logged in
#3
hello, you must use the formula
A=\frac{1}{2}\int_{\phi_1^}^{\phi_2}r^2\,d\phi
Sonnhard.

PostPosted: Sat Oct 31, 2009 10:22 am  Back to top 
  ProfilePM
Display posts from previous:   Sort by:   
3 Posts • Page 1 of 1
Post new topic   Reply to topic View previous topicView next topic
Home » College Playground » Calculus - Real Analysis » Calculus Computations and Tutorials
 
Jump to:  


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum
You cannot attach files in this forum
You can download files in this forum
You cannot post calendar events in this forum


© Copyright 2008 AoPS Incorporated. All Rights Reserved. • Foundation • Privacy • Contact Us