'''

length_curve.py

Find the length of a curve between two points

'''

from sympy import Derivative, Integral, Symbol, sqrt, SympifyError, sympify

def find_length(fx, var, a, b):

deriv = Derivative(fx, var).doit()

length = Integral(sqrt(1+deriv**2), (var, a, b)).doit().evalf()

return length

if __name__ == '__main__':

f = input('Enter a function in one variable: ')

var = input('Enter the variable: ')

l = float(input('Enter the lower limit of the variable: '))

u = float(input('Enter the upper limit of the variable: '))

try:

f = sympify(f)

except SympifyError:

print('Invalid function entered')

else:

var = Symbol(var)

print('Length of {0} between {1} and {2} is: {3} '.

format(f, l, u, find_length(f, var, l, u)))