February 23rd, 2009, 12:54 PM  #1 
Newbie Joined: Feb 2009 Posts: 2 Thanks: 0  Length curve
Hello I have a function, and need to find the distance of that polynomial function. Not sure how to do this any help. Notes: I think its a degree four, it might be a three, i have five points. Starting fron the origin, (0,0) Point O, Point A (2,2), Point B (6, 2.15) point c (10,3) Point E (16,7). Im not really good at this stuff. Put it in my calculator and get this a= 6.555e03 b=0.1810119 c=1.44681547 d=3.2220238 e=5.902e11 and r^2=1 Below it, it says y=ax^4+bx^3+cx^2+dx+e so i figure i sub a,b,c,d,e into that, and that how i get my function y=6.555e03x^4  0.1810119x^3 + 1.44681547x^2  3.2220238x + 5.902e11 So how do i use this in that arc length formula, dad said to use string lol These may help http://www.mathwords.com/a/arc_length_of_a_curve.htm http://www.maths.abdn.ac.uk/~igc/tch/ma ... ode21.html 
February 23rd, 2009, 02:05 PM  #2 
Member Joined: Feb 2009 Posts: 34 Thanks: 0  Re: Length curve
hi watty08 using your points you can calculate the parameters of your polynom aX^4+bX^3+cX^2+dX+e If they are points laying on your curve it mean than for example for the first points O(0,0) that mean you plug 0 you have to get 0 so f(0)=0 so e=0 for the other point A(2,2) mean f(2)=2 that mean you plug 2 you have to get 2 so 16a+8b+4c+2d=2 and so on You arrive at a system eq with 4 eq and 4 unknown variable a, b, c, d (e=0) the system is: 16a+8b+4c+2d=2; 1296a+216b+36c+6d=2.15; 10000a+1000b+100c+10d=3; 65536a+4096b+256c+16d=7 I get the solution for you a=0.0066; b=0.1810; c=1.4468; d=3.222; if you plug those numbers in your system every eq is satisfied Ok i think is still a problem with your number here because everything should be very simple you have to check this...So your function is f(x)=0.0066X^40.1810X^3+1.4468X^23.222X a little bit nasty because you have to do it's derivative df/dx and after that the length is L=integral from 0 to 16 (your last coord point) from (sqrt(1+[df/dx]^2)) is very complicate to do this if the function is not very simple that you can get off the square root Good luck Check your numbers again 
February 23rd, 2009, 09:08 PM  #3 
Newbie Joined: Feb 2009 Posts: 2 Thanks: 0  Re: Length curve
How did you get a,b,c,d did you get them by using similtanious equations> Are you also saying that i differentiate the f(x)=0.0066X^40.1810X^3+1.4468X^23.222X And then sub that into the equation (sqrt(1+[df/dx]^2)) If so wont i still have the X's left over. Thanks heaps for your help 
February 24th, 2009, 05:07 AM  #4  
Member Joined: Feb 2008 Posts: 44 Thanks: 0  Re: Length curve Quote:
Quote:
Arc length for this problem is:  

Tags 
curve, length 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
the length of the curve  luketapis  Calculus  3  March 5th, 2012 06:59 PM 
Length of a curve  snopy  Calculus  2  January 7th, 2011 08:22 AM 
Length of a curve  snopy  Calculus  5  December 13th, 2010 07:21 AM 
Length of a curve  Ahplym  Calculus  2  December 5th, 2010 09:50 AM 
curve length  Haytham  Real Analysis  0  July 20th, 2009 09:01 AM 