from matplotlib.patches import Polygon
import matplotlib.pyplot as plt
import numpy as np

# 定义一个求积分的函数
def func(x):
 return 0.3* (x**2) + (0.1*x) + 1

# 定义积分区间
a, b = 1,2
x = np.linspace(0,3)
y = func(x)

# 绘制曲线
fig, ax = plt.subplots(figsize=(14,8))
plt.plot(x, y, 'g')
plt.ylim(ymin=0)

# 使用Polygon生成阴影部分
Ix = np.linspace(a, b)
Iy = func(Ix)
verts = [(a, 0)] + list(zip(Ix, Iy)) + [(b, 0)]
ploy = Polygon(verts, facecolor = '0.7', edgecolor='0.5')
ax.add_patch(ploy)

# 添加数学公式和坐标轴标签
# r" "中间为LaTex语法表示的公式
plt.text(0.5 * (a+b), 1, r"$\int_a^b f(x)\mathrm{d}x$",
  horizontalalignment='center', fontsize=20)
# 前两个参数是放置文本的坐标
plt.figtext(0.9, 0.075,'$x$')
plt.figtext(0.075,0.9,'$f(x)$' )

ax.set_xticks((a,b))
ax.set_xticklabels(('$a$','b'))
ax.set_yticks((func(a), func(b)))
ax.set_yticklabels(('f(a)','f(b)'))
plt.grid(True)
plt.show()

import numpy as np
import matplotlib
matplotlib.rcParams['text.usetex'] = True
import matplotlib.pyplot as plt


t = np.linspace(0.0, 1.0, 100)
s = np.cos(4 * np.pi * t) + 2

fig, ax = plt.subplots(figsize=(6, 4), tight_layout=True)
ax.plot(t, s)

ax.set_xlabel(r'\textbf{time (s)}')
ax.set_ylabel('\\textit{Velocity (\N{DEGREE SIGN}/sec)}', fontsize=16)
ax.set_title(r'\TeX\ is Number $\displaystyle\sum_{n=1}^\infty'
    r'\frac{-e^{i\pi}}{2^n}$!', fontsize=16, color='r')
plt.show()