함수의 그래프: 부정적분

다음 그림들은 전자책 파이썬과 함께하는 미분적분의 6.1장에 수록된 그래프들과 코드들입니다.

import numpy as np 
import pandas as pd
from sympy import *
import matplotlib.pyplot as plt
import seaborn as sns
sns.set_style("darkgrid")

def axisTran(ax):
    ax.spines['left'].set_position(("data", 0))
    ax.spines['bottom'].set_position(("data", 0))
    ax.spines['right'].set_visible(False)
    ax.spines['top'].set_visible(False)

#그림 6.1.1
x=np.linspace(0, 3, 100)
y=3*x
plt.figure(figsize=(4,3))
plt.plot(x, y, color="g", lw=3, label="f(x)=3x")
plt.fill_between(x, y, alpha=0.6)
plt.xlabel("Time(hr)", fontsize="11")
plt.ylabel("Vel\n(km/hr)",  rotation="horizontal", fontsize="11", labelpad=20)
plt.legend(loc=(0.2, 0.9), labelcolor='g', frameon=False)
plt.show()

#그림 6.1.2
x=[0, 50, 125, 200]
y=[400, 400, 300, 250]
fig, ax=plt.subplots(figsize=(4,3))
ax.step(x, y, 'g')
ax.fill_between(np.linspace(0, 50, 50), np.repeat(400, 50), color="b", alpha=0.3)
ax.fill_between(np.linspace(50,125, 50), np.repeat(300, 50), color="r", alpha=0.3)
ax.fill_between(np.linspace(125, 200), np.repeat(250, 50), color="orange", alpha=0.3)
axisTran(ax)
ax.set_xlabel("# of product", fontsize=11)
ax.set_ylabel("cost", rotation="horizontal", labelpad=20, fontsize=11)
ax.text(0, 350, "C(x)=400", color="b")
ax.text(55, 250, "C(x)=300", color="r")
ax.text(130, 200, "C(x)=400", color="brown")
plt.show()

#그림 6.1.3
a=symbols("a")
f=(a-1)*(a-2)*(a-4)+3
x=np.linspace(0, 5, 100)
y=[f.subs(a, i) for i in x]
fig, ax=plt.subplots(figsize=(4,3))
ax.plot(x, y ,color="g", label="(x-1)(x-2)(x-4)+3")
x0=np.linspace(1, 4, 10)
for i in range(1, len(x0)):
    xrng=np.linspace(x0[i-1], x0[i], 20)
    y0=np.repeat(float(f.subs(a, x0[i-1])), 20)
    ax.fill_between(xrng, y0, color="b", alpha=0.3)
axisTran(ax)
ax.set_xlabel("x", fontsize=11)
ax.set_ylabel("f(x)", rotation="horizontal", labelpad=10, fontsize=11)
ax.set_ylim((-1, 4))
ax.legend(loc=(0.8, 0.8), labelcolor="g", frameon=False)
plt.show()

#그림 6.1.4
a=symbols("a")
f=600*a-a**2
x=np.linspace(0, 600, 100)
y=[f.subs(a, i ) for i in x]
fig, ax=plt.subplots(figsize=(4,3))
ax.plot(x, y ,color="g", label=r"$f(x)=600x-x^2$")
x0=np.linspace(0, 600, 7)
for i in range(1, len(x0)):
    xrng=np.linspace(x0[i-1], x0[i], 20)
    y0=np.repeat(float(f.subs(a, x0[i])), 20)
    ax.fill_between(xrng, y0, color="brown", alpha=0.3)
axisTran(ax)
ax.set_xlabel("x", fontsize=11)
ax.set_ylabel("f(x)", rotation="horizontal", labelpad=10, fontsize=11)
ax.legend(loc=(0.8, 0.8), labelcolor="g", frameon=False)
plt.show()

#그림 6.1.5
a=symbols("a")
f=600*a-a**2
x=np.linspace(0, 600, 100)
y=[f.subs(a, i ) for i in x]
fig, ax=plt.subplots(figsize=(4,3))
ax.plot(x, y ,color="g", label=r"$f(x)=600x-x^2$")
x0=np.linspace(0, 600, 61)
for i in range(1, len(x0)):
    xrng=np.linspace(x0[i-1], x0[i], 20)
    y0=np.repeat(float(f.subs(a, x0[i])), 20)
    ax.fill_between(xrng, y0, color="brown", alpha=0.3)
axisTran(ax)
ax.set_xlabel("x", fontsize=11)
ax.set_ylabel("f(x)", rotation="horizontal", labelpad=10, fontsize=11)
ax.legend(loc=(0.8, 0.8), labelcolor="g", frameon=False)
plt.show()