My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Thanks Tree3Thanks
  • 1 Post By skeeter
  • 1 Post By Country Boy
  • 1 Post By Country Boy
Reply
 
LinkBack Thread Tools Display Modes
June 25th, 2017, 03:37 PM   #1
Newbie
 
Joined: Jun 2017
From: Tennessee

Posts: 1
Thanks: 0

Circumference of an Ellipse

Approximate, within an error of 0.001 units, the circumference of the ellipse given by the equation

(x/3)^2+(y/2)^2=1
terminus is offline  
 
June 25th, 2017, 04:19 PM   #2
Math Team
 
Joined: Jul 2011
From: Texas

Posts: 2,663
Thanks: 1328

$x = 3\cos{t}$

$y = 2\sin{t}$

$\displaystyle C = 4\int_0^{\pi/2} \sqrt{\left(\dfrac{dx}{dt}\right)^2 + \left(\dfrac{dy}{dt} \right)^2} \, dt$

$\displaystyle C = 4 \int_0^{\pi/2} \sqrt{9\sin^2{t}+4\cos^2{t}} \, dt \approx 15.865$
Thanks from Country Boy
skeeter is offline  
July 1st, 2017, 11:07 AM   #3
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 2,829
Thanks: 753

The reason the problem asks you to "Approximate, within an error of 0.001 units" is that we cannot do this integral "analytically". It is one of a class of integrals called "elliptic integrals". I remember, many, many years ago seeing. in a University library, an entire shelf of, I think, 20 large volumes giving numerical values of the elliptic integrals. You will need to complete this problem using some numerical integration method.
Thanks from 123qwerty
Country Boy is offline  
July 1st, 2017, 11:17 AM   #4
Senior Member
 
Joined: Dec 2012
From: Hong Kong

Posts: 853
Thanks: 311

Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics
Quote:
Originally Posted by Country Boy View Post
The reason the problem asks you to "Approximate, within an error of 0.001 units" is that we cannot do this integral "analytically". It is one of a class of integrals called "elliptic integrals". I remember, many, many years ago seeing. in a University library, an entire shelf of, I think, 20 large volumes giving numerical values of the elliptic integrals. You will need to complete this problem using some numerical integration method.
20 large volumes! How times have changed with the advent of computers...
123qwerty is offline  
July 1st, 2017, 05:45 PM   #5
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 2,829
Thanks: 753

Quote:
Originally Posted by 123qwerty View Post
20 large volumes! How times have changed with the advent of computers...
This was in 1970 and the numbers in those volumes had been calculated by computer. But it was much easier to carry the relevant volume around with you than to carry a computer!
Thanks from 123qwerty
Country Boy is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
circumference, ellipse



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Why do we use 22/7 for circumference and not pi? Opposite Geometry 7 August 29th, 2014 03:06 PM
Circumference of a circle Chikis Elementary Math 7 January 22nd, 2014 05:46 PM
ellipse circumference kapital Calculus 22 August 6th, 2012 10:53 AM
Circumference Problem matemego Algebra 3 November 3rd, 2011 10:25 PM
Ellipse Ellipse Intersection tom-9000 Algebra 1 June 17th, 2009 02:40 PM





Copyright © 2017 My Math Forum. All rights reserved.