Code to find the volume of the tetrahedron bounded by:

x = 0,\quad y = 0,\quad z = 0,\quad ax + by + cz = 1

2.c) Write the code to find the volume of the tetrahedron bounded by x = 0,\quad y = 0,\quad z = 0,\quad ax + by + cz = 1 using Mathematical tools.

Answer:

from sympy import symbols, integrate, pprint

# Define symbols
x, y, z = symbols('x y z')
a, b, c = symbols('a b c')

# Define the volume integral
volume = integrate(
    1,                          # Function to integrate
    (z, 0, c * (1 - x/a - y/b)),  # Limits for z
    (y, 0, b * (1 - x/a)),        # Limits for y
    (x, 0, a)                     # Limits for x
)

# Pretty print the result
pprint(volume)