习题7.1

import numpy as np
import scipy.interpolate as spi
import scipy.integrate as spi_integrate

def g(x):
    return ((3*x**2 + 4*x + 6) * np.sin(x)) / (x**2 + 8*x + 6)

# 生成x值
x_values = np.linspace(0, 10, 1000)

# 计算对应的y值
y_values = g(x_values)

# 创建三次样条插值
spline = spi.CubicSpline(x_values, y_values)

def h(x):
    return spline(x)

# 积分g(x)从0到10
integral_g, _ = spi_integrate.quad(g, 0, 10)

# 生成更细的x值
x_fine = np.linspace(0, 10, 10000)
# 计算对应的y值
y_fine = h(x_fine)
# 积分h(x)从0到10
integral_h = np.trapz(y_fine, x_fine)

# 打印结果
print(f"积分 g(x) 从 0 到 10 的结果: {integral_g}")
print(f"积分 h(x) 从 0 到 10 的结果: {integral_h}")

print("学号：3008")

结果如下图所示