Double Integral Over Region Graph Example

import micropip
await micropip.install("matplotlib")
await micropip.install("numpy")
 
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
 
# Create figure
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
 
# Define the plane: z = f(x, y)
def plane(x, y):
    return x + y  # Example linear plane
 
# Define the region R in xy-plane (x, y bounds)
x = np.linspace(0, 1, 100)
y = np.linspace(0, 1, 100)
x, y = np.meshgrid(x, y)
 
# Mask or define the region (for simplicity, using a circular region here)
R = np.sqrt(x**2 + y**2) <= 0.5  # Circular region
z = plane(x, y) * R  # Apply mask to the plane
 
# Plot the plane over the region
ax.plot_surface(x, y, z, color='blue', alpha=0.6, rstride=100, cstride=100)
 
# Projection of the region onto the xy-plane (the green region)
ax.plot_surface(x, y, np.zeros_like(z), where=R, color='green', alpha=0.3)
 
# Plot the vertical lines (from the xy-plane to the surface)
ax.plot_wireframe(x, y, z, color='green', alpha=0.3)
 
# Set axis labels
ax.set_xlabel('X-axis')
ax.set_ylabel('Y-axis')
ax.set_zlabel('Z-axis')
 
# Show plot
plt.show()