(参考)モンテカルロ法で楕円の面積を求めてみる
https://qiita.com/jp_yen/items/5d561ada97dd4fc6d558
(参考)Ellipses>area
https://docs.sympy.org/latest/modules/geometry/ellipses.html
(参考)高校数学の美しい物語>楕円の面積公式の3通りの導出
https://mathtrain.jp/sofdaen
fullscript.py
from sympy import *
p1 = Point(0, 0)
e1 = Ellipse(p1, 160, 90)
print(e1.area) # 14400*pi
print(float(e1.area)) # 45238.93421169302
#
var("x, y, a, b")
p1 = Point(x, y)
e1 = Ellipse(p1, a, b)
print(e1.area) # pi*a*b
print(float(e1.area.subs(a,160).subs(b,90))) # 45238.93421169302
#
var("aa, bb")
f=4*bb*(1-x**2/aa**2)**(1/2)
print(integrate(f, (x, 0, aa))) #4.0*aa*bb*hyper((-0.5, 1/2), (3/2,), exp_polar(2*I*pi))