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Thread Subject:
length of the arc

Subject: length of the arc

From: rsch tosh

Date: 14 Mar, 2012 20:23:20

Message: 1 of 4

Hi could anyone help me with this ques

y=x^3/25-3*x^2/625-2*x/15625

I want to find the length of this equation using matlab. Please help

Subject: length of the arc

From: TideMan

Date: 14 Mar, 2012 20:31:30

Message: 2 of 4

On Thursday, March 15, 2012 9:23:20 AM UTC+13, rsch tosh wrote:
> Hi could anyone help me with this ques
>
> y=x^3/25-3*x^2/625-2*x/15625
>
> I want to find the length of this equation using matlab. Please help

eqn='y=x^3/25-3*x^2/625-2*x/15625';
length(eqn)
The answer is 28.

Subject: length of the arc

From: Nasser M. Abbasi

Date: 14 Mar, 2012 21:07:24

Message: 3 of 4

On 3/14/2012 3:23 PM, rsch tosh wrote:
> Hi could anyone help me with this ques
>
> y=x^3/25-3*x^2/625-2*x/15625
>
> I want to find the length of this equation using matlab. Please help


use the arc length formula, and integrate it using quad:

----------------------
  syms y x
  y = x^3/25-3*x^2/625-2*x/15625;
  integrand = sqrt(1+(diff(y,x))^2)
---------------------

((- (3*x^2)/25 + (6*x)/625 + 2/15625)^2 + 1)^(1/2)

so the above is the function you need to integrate. Use
numerical integration. Make a function and apply quad:

-----------------------
myfun = @(x) ((- (3*x.^2)/25 + (6*x)/625 + 2/15625).^2 + 1).^(1/2)
  from = 0;
  to = 2;
  Q = quad(myfun,from,to)
-------------------

Q =
     2.0404

so, the length is about 2.

  ezplot('x^3/25-3*x^2/625-2*x/15625',[0,2])

--Nasser

Subject: length of the arc

From: Roger Stafford

Date: 15 Mar, 2012 01:45:17

Message: 4 of 4

"rsch tosh" wrote in message <jjquno$knf$1@newscl01ah.mathworks.com>...
> y=x^3/25-3*x^2/625-2*x/15625
> I want to find the length of this equation using matlab.
- - - - - - - - -
  The integral that gives the arc length of your curve is known in general as an "elliptic integral". As Nasser has shown, in your case it is the integral of the square root of a certain quartic polynomial. See:

 http://mathworld.wolfram.com/EllipticIntegral.html, and
 http://en.wikipedia.org/wiki/Elliptic_integral

for a discussion. Elliptic integrals first became of interest in the problem of finding arc length along an ellipse, hence the name.

Roger Stafford

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