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Area Under a Curve Algorithm #1701

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Merged
merged 12 commits into from
Jan 19, 2020
55 changes: 55 additions & 0 deletions maths/area_under_curve.py
Original file line number Diff line number Diff line change
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"""
Approximates the area under the curve using the trapezoidal rule
"""

from typing import Callable, Union

def trapezoidal_area(fnc: Callable[[Union[int, float]], Union[int, float]],
x_start: Union[int, float],
x_end: Union[int, float],
steps: int = 100) -> float:
"""
Treats curve as a collection of linear lines and sums the area of the
trapezium shape they form
:param fnc: a function which defines a curve
:param x_start: left end point to indicate the start of line segment
:param x_end: right end point to indicate end of line segment
:param steps: an accuracy gauge; more steps increases the accuracy
:return: a float representing the length of the curve

>>> def f(x):
... return 5
>>> f"{trapezoidal_area(f, 12.0, 14.0, 1000):.3f}"
'10.000'
>>> def f(x):
... return 9*x**2
>>> f"{trapezoidal_area(f, -4.0, 0, 10000):.4f}"
'192.0000'
>>> f"{trapezoidal_area(f, -4.0, 4.0, 10000):.4f}"
'384.0000'
"""
x1 = x_start
fx1 = fnc(x_start)
area = 0.0
for i in range(steps):
# Approximates small segments of curve as linear and solve
# for trapezoidal area
x2 = (x_end - x_start)/steps + x1
fx2 = fnc(x2)
area += abs(fx2 + fx1) * (x2 - x1)/2
# Increment step
x1 = x2
fx1 = fx2
return area


if __name__ == "__main__":
def f(x):
return x**3 + x**2

print("f(x) = x^3 + x^2")
print("The area between the curve, x = -5, x = 5 and the x axis is:")
i = 10
while i <= 100000:
print(f"with {i} steps: {trapezoidal_area(f, -5, 5, i)}")
i*=10