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# 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 numpy as np
    import matplotlib.pyplot as plt
    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()
    plt.plot(x, y, 'r', linewidth=2)
    plt.ylim(ymin=0)

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

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

    plt.figtext(0.9, 0.05, '$x$')
    plt.figtext(0.1, 0.9, '$y$')

    ax.spines['right'].set_visible(False)
    ax.spines['top'].set_visible(False)
    ax.xaxis.set_ticks_position('bottom')

    ax.set_xticks((a, b))
    ax.set_xticklabels(('$a$', '$b$'))
    ax.set_yticks([])

    plt.show()

Total running time of the script: ( 0 minutes 0.024 seconds)

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