calculate a dobule integral using naive approach

double-integral.py

#
# calculate a dobule integral using naive approach
# python 3.13.0
#
# analytical solution of the example below is -7
#   step 0.0100: -6.9976327434199135 (44 ms)
#   step 0.0010: -7.000145573771798  (2.7 s)
#   step 0.0001: -7.000002405139909  (4 m 49 s)
#
# possible improvements
#  - adapt it to use decimal
#  - rewrite in C
#
from math import sqrt, ceil

# define bounds of where the area lies
xstart = 0.0
xend = 2.0
ystart = -2.0
yend = 2.0

# 0.01 - fast, 0.001 - doable, 0.0001 - takes ages
step = 0.0001

# function to integrate
def f(x, y):
    return y - 2 * x * sqrt(x ** 2 + y ** 2)

# area to integrate over (return true for x, y if the point is in the area)
def area(x, y):
    return 3 <= x ** 2 + y ** 2 <= 4 and x >= 0


# don't change the below

output = 0.0
for xi in range(ceil((xend - xstart) / step)):
    for yi in range(ceil((yend - ystart) // step)):
        x = xstart + xi * step
        y = ystart + yi * step
        if area(x, y):
            output += f(x, y) * step * step
print(output)