2.c) Write the code to find the area of an ellipse by double integration: A = 4 \int_{0}^{a} \int_{0}^{b \sqrt{1 - \frac{x^2}{a^2}}} dy,dx
Answer:
from sympy import symbols, integrate, sqrt, pprint
x, y = symbols('x y')
a = 4
b = 6
# Define the upper limit of the inner integral properly
upper_limit = (b / a) * sqrt(a**2 - x**2)
# Compute the area using double integration
Area = 4 * integrate(integrate(1, (y, 0, upper_limit)), (x, 0, a))
# Pretty print the result
pprint(Area)