Code:
import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(-2.5, 2.5, 400)
y = np.abs(x**2 - 1)
plt.figure(figsize=(8, 5))
plt.plot(x, y, 'b-', label=r'$y = |x^2 - 1|$')
plt.axhline(0, color='black', linewidth=1)
plt.axvline(0, color='black', linewidth=1)
# Fill the area
x_fill = np.linspace(-2, 2, 400)
y_fill = np.abs(x_fill**2 - 1)
plt.fill_between(x_fill, y_fill, color='skyblue', alpha=0.4, label='Area = 4')
plt.title('Area under $y = |x^2 - 1|$ from $x = -2$ to $x = 2$')
plt.xlabel('x')
plt.ylabel('y')
plt.grid(True, linestyle='--', alpha=0.7)
plt.legend()
plt.xlim(-2.5, 2.5)
plt.ylim(0, 3.5)
plt.savefig('plot.png')
Output:
(No output)
