Volumes of Revolution in Python

Python Code:

#Volume of the ellipsoid formed by rotating y=b/a * sqrt(a^2-x^2) about the x-axis
from sympy import *

x=symbols('x')
a,b=symbols('a b')
f=b/a*sqrt(a**2-x**2)

fplot=f.subs({a:3,b:4})
print(fplot)

matplotlib notebook

plot(fplot,(x,-3,3))

c=solve(f,x)
print(c)

Volume=integrate(pi*f**2,(x,c[0],c[1]))
print('The volume of the ellipsoid is',Volume.simplify())

Open Python Notebook File