'''
Author: SJ2050
Date: 2021-10-29 19:29:51
LastEditTime: 2021-10-29 19:50:31
Version: v0.0.1
Description: Solution for homework2.1.
Copyright © 2021 SJ2050
'''
import numpy as np
from matplotlib import pyplot as plt

if __name__ == '__main__':
    y_func = lambda x: (x-1)**2+2
    N = 50
    xs = np.linspace(-5, 5, num=N+1)
    ys = np.array([y_func(x) for x in xs])

    integrate_sum = 0
    for i in range(N):
        plt.plot([xs[i], xs[i]], [0, ys[i]], color='black')
        plt.plot([xs[i], xs[i+1]], [ys[i], ys[i+1]], color='black')
        plt.plot([xs[i+1], xs[i+1]], [ys[i+1], 0], color='black')
        integrate_sum += 0.5*(ys[i]+ys[i+1])*(xs[i+1]-xs[i])

    plt.plot(xs, ys, color='green')
    plt.ylim(0, 40)
    plt.show()
    print(f'(x-1)^2+2在[-5, 5]区间上使用梯形求积为: {integrate_sum}')