Error while calculating arc length of curve in Fortran

[NicolasPan]

The program must calculate the length of the curve of ƒ=3.1*x^2-5.3/x between x=1/2 and x=3/2.The legth should be calculated as the sum of n line segments starting with n=1 and ending with n=20.

I really can't find why the result I'm getting is wrong.Thanks in advance
I am giving you the code below:

program pr2_ex2
implicit none
integer::x
double precision::dy,dx !dy=the height of the linear part & dx=the length of the linear part
double precision::x1,x2,s !f=f(x) the function,x=the values which can be given to f
double precision::length 
  print*,"Please enter the function's starting point"
  read*,x1
  print*,"Please enter the function's ending  point"
  read*,x2
length=0
  s=0
do x=2,21
   dx=((x*abs(x2-x1)-(x-1)*abs(x2-x1))/(20))
   dy=(3.1*(x*abs(x2-x1)/20)**2-(5.3*20/x*abs(x2-x1)))-(3.1*((x-1)*abs(x2-x1)/20)**2-(5.3*20/(x-1)*abs(x2-x1)))
   length=sqrt((dx**2)+(dy**2))
   s=length+s
   end do
   print*,s
end program

 

[NascentOxygen]

What is the result you're getting that you say is wrong?

"Lenght" being a misspelling of "length"?

 

[NicolasPan]

Well if for x1=0.5 and for x2=1.5 I am getting 104.3853... That can't be right since I've checked it in wolframalpha and it says 13

 

[NascentOxygen]

The program must calculate the length of the curve of ƒ=3.1*x^2-5.3/x between x=1/2 and x=3/2.The leght should be calculated as the sum of n line segments starting with n=1 and ending with n=20.

EDIT: My reading of this is that it needs a program to print out 20 answers, one answer for each value of n.

I can see your program prints only one answer, right at the end, so that might be where you are going wrong?

How would you explain to someone what n is in this situation, to show you understand what this calculation is about?

 

[NicolasPan]

My reading of this is that your program will print out 20 answers, one answer for each value of n.

I can see your program prints only one answer, right at the end, so that might be where you are going wrong?

How would you explain to someone what n is in this situation, to show you understand what this calculation is about?

Well I think the curve's x's from x1 to x2 can be divided to 20 equidistant x's with every n to be used to get to the next x.Xn=abs(x2-x1)*x/20 and X(n-1)=(x-1)*(abs(x2-x1)/20).Therefore if I subtract Xn,X(n-1),I will be getting the distance between consecutive X's.

 

[NascentOxygen]

Well I think the curve's x's from x1 to x2 can be divided to 20 equidistant x's with every n to be used to get to the next x.Xn=abs(x2-x1)*x/20 and X(n-1)=(x-1)*(abs(x2-x1)/20).Therefore if I subtract Xn,X(n-1),I will be getting the distance between consecutive X's.

That would be the case for n=20. But, for example, when n=16 then there would be 16 segments spanning the path between those same two endpoints. That's what I think. The greater the value of n, the closer to the true length will be your approximation.

 

[NicolasPan]

I am aware of that,although that can't be the problem the bigger the n the more my sum goes up.And the problem states that it should be able to work with just n=20,which doesn't in my case.Therefore I assume the problem is associated with my code.Nevermind thanks for your suggestion

 

[DrClaude]

dy=(3.1*(x*abs(x2-x1)/20)**2-(5.3*20/x*abs(x2-x1)))-(3.1*((x-1)*abs(x2-x1)/20)**2-(5.3*20/(x-1)*abs(x2-x1)))

When you write 5.3*20/x*abs(x2-x1), it means
$$
5.3 \times \frac{20}{x} \times \left| x_2 - x_1 \right|
$$
which is not what you want.

You should create a function that given x, returns f(x), instead of hard-coding it many times. Also, do not use x as an integer index for the loop. It looks too much like the mathematical variable x. Use something like i instead.

 

[Mark44]

The program must calculate the length of the curve of ƒ=3.1*x^2-5.3/x between x=1/2 and x=3/2.The legth should be calculated as the sum of n line segments starting with n=1 and ending with n=20.

I really can't find why the result I'm getting is wrong.Thanks in advance
I am giving you the code below:

program pr2_ex2
implicit none
integer::x
double precision::dy,dx !dy=the height of the linear part & dx=the length of the linear part
double precision::x1,x2,s !f=f(x) the function,x=the values which can be given to f
double precision::length
  print*,"Please enter the function's starting point"
  read*,x1
  print*,"Please enter the function's ending  point"
  read*,x2
length=0
  s=0
do x=2,21
   dx=((x*abs(x2-x1)-(x-1)*abs(x2-x1))/(20))
   dy=(3.1*(x*abs(x2-x1)/20)**2-(5.3*20/x*abs(x2-x1)))-(3.1*((x-1)*abs(x2-x1)/20)**2-(5.3*20/(x-1)*abs(x2-x1)))
   length=sqrt((dx**2)+(dy**2))
   s=length+s
   end do
   print*,s
end program

Nicholas, your code is chock full of what are disparagingly called "magic" numbers, constants that are hard-coded. The number of subintervals should be a variable that the user enters, and not sprinkled throughout in your loop ending value and your assignment statements for dx and dy.

As already suggested, your code would be a lot more readable if you used a function to calculate the y values.

function f(x)
   double precision :: f
   double precision ::x
 
   f = 3.1 * x**2 - 5.3/x
   return
end function

The only change to your main program would be to insert a declaration for the function up near the top:

program pr2_ex2
implicit none
double precision:: f

To use the function, write an expression of the form f(x1).

One more thing -- you really shouldn't use x as your loop control variable. Use i or j for that.

 

[NicolasPan]

Thank you for your answers! I will be using your advice for sure in my code and see how it goes

 

[Mark44]

I put together some Python code to do this calculation. With n = 20 and n = 100 subintervals, I got 13.3059 in the first four decimal places.