# Integral as the area under a curve#

Although this is a simple example, it demonstrates some important tweaks:

• A simple line plot with custom color and line width.

• A shaded region created using a Polygon patch.

• A text label with mathtext rendering.

• figtext calls to label the x- and y-axes.

• Use of axis spines to hide the top and right spines.

• Custom tick placement and labels.

import matplotlib.pyplot as plt
import numpy as np

from matplotlib.patches import Polygon

def func(x):
return (x - 3) * (x - 5) * (x - 7) + 85

a, b = 2, 9  # integral limits
x = np.linspace(0, 10)
y = func(x)

fig, ax = plt.subplots()
ax.plot(x, y, 'r', linewidth=2)
ax.set_ylim(bottom=0)

# Make the shaded region
ix = np.linspace(a, b)
iy = func(ix)
verts = [(a, 0), *zip(ix, iy), (b, 0)]
poly = Polygon(verts, facecolor='0.9', edgecolor='0.5')

ax.text(0.5 * (a + b), 30, r"$\int_a^b f(x)\mathrm{d}x$",
horizontalalignment='center', fontsize=20)

fig.text(0.9, 0.05, '$x$')
fig.text(0.1, 0.9, '$y$')

ax.spines[['top', 'right']].set_visible(False)
ax.set_xticks([a, b], labels=['$a$', '$b$'])
ax.set_yticks([])

plt.show()

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