함수의 그래프: 정적분

다음 그림들은 전자책 파이썬과 함께하는 미분적분의 6.3장과 6.4장에 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 6.3.1
a=symbols("a")
f=(a-1)*(a-2)*(a-3)+3
x=np.linspace(0, 5, 100)
y=[f.subs(a, i) for i in x]
plt.figure(figsize=(4,3))
plt.plot(x, y ,color="g", label="f(x)")
x0, x1=np.linspace(1, 2.5, 20), np.linspace(2.5, 4, 20)
fy0, fy1=[float(f.subs(a, i)) for i in x0], [float(f.subs(a, i)) for i in x1]
plt.fill_between(x0, fy0, color="b", alpha=0.5, label="F(x)")
plt.fill_between(x1, fy1, color="r", alpha=0.5, label="F(x+h)-F(X)")
plt.xticks([1, 2.5, 4], ["a=0", "x", "b=x+h"])
plt.yticks([])
plt.ylabel("f(x)", rotation="horizontal", labelpad=10, fontsize=11)
plt.ylim((-3, 10))
plt.legend(loc='best', labelcolor="linecolor", frameon=False)
plt.show()

#그림 6.3.2
a=symbols("a")
f=a**2-1
x=np.linspace(-1, 2.5, 100)
y=[float(f.subs(a, i)) for i in x]
plt.figure(figsize=(4,3))
plt.plot(x, y ,color="g", label=r"$f(x)=x^2-1$")
x1=np.linspace(0, 2, 100)
y1=[float(f.subs(a, i)) for i in x1]
plt.fill_between(x1, y1,color="b", alpha=0.3)
plt.xlabel("x", fontsize=11)
plt.ylabel("f(x)", rotation="horizontal", labelpad=10, fontsize=11)
plt.ylim((-2, 3))
plt.legend(loc="best", labelcolor=["g", 'b','r'], frameon=False)
plt.show()

#그림 6.3.3
t=symbols('t')
a=12*t**2-6
v=a.integrate(t)+5
s=v.integrate(t)+5
x=np.linspace(-4, 4, 100)
ay=[a.subs(t, i) for i in x]
vy=[v.subs(t, i) for i in x]
sy=[s.subs(t, i) for i in x]
plt.figure(figsize=(4,3))
plt.plot(x, ay, color="r", label="a(t)")
plt.plot(x, vy, color="b", label="v(t)")
plt.plot(x, sy, color="g", label="s(t)")
plt.ylim(-10, 40)
plt.xlabel("x", fontsize=11)
plt.ylabel("y", rotation="horizontal", fontsize=11)
plt.legend(loc="best", labelcolor='linecolor', frameon=False)
plt.show()

#그림 6.3.5
x=np.arange(0, 360)
r=np.cos(np.radians(x))+1
plt.figure(figsize=(4,3))
plt.plot(x, r ,color="g", label=r"$r(\theta)=\cos(\theta)+1$")
x0=np.linspace(0, 90, 50)
r0=np.cos(np.radians(x0))+1
plt.fill_between(x0, r0, color="r", alpha=0.3)
plt.xticks([0, 90, 180, 270, 360], [0, r"$\frac{\pi}{2}$", r"$\pi$", r"$\frac{3\pi}{2}$", r"$2\pi$" ])
plt.xlabel(r"$\theta$", fontsize=11)
plt.ylabel(r"$r(\theta)$", rotation="horizontal",  labelpad=10, fontsize=11)
plt.legend(loc="best", labelcolor="g", frameon=False)
plt.show()

#그림 6.3.6
x=np.linspace(-1, 2.5, 100)
f=2*x+1
g=x**2+1
plt.figure(figsize=(4,3))
plt.plot(x, f ,color="b", label=r"$f(x)=2x+1$")
plt.plot(x, g ,color="g", label=r"$g(x)=x^2+1$")
x1=np.linspace(0, 2, 100)
f1=2*x1+1
g1=x1**2+1
plt.fill_between(x1, f1, g1, color="r", alpha=0.3)
plt.xlabel("x", fontsize=11)
plt.ylabel("y", rotation="horizontal", labelpad=10, fontsize=11)
plt.legend(loc="best", labelcolor="linecolor", frameon=False)
plt.show()

#그림 6.3.7
x=np.linspace(-3, 10, 100)
f=x**4-3*x**3-4*x**2+10
g=40-x**2
plt.figure(figsize=(4,3))
plt.plot(x, f ,color="b", label=r"$f(x)=2x+1$")
plt.plot(x, g ,color="g", label=r"$g(x)=x^2+1$")
x1=np.linspace(1,3, 100)
f1=x1**4-3*x1**3-4*x1**2+10
g1=40-x1**2
plt.fill_between(x1, g1, f1, color="r", alpha=0.3)
plt.xlabel("x", fontsize=11)
plt.ylabel("y", rotation="horizontal", labelpad=10, fontsize=11)
plt.ylim((-40, 60))
plt.legend(loc="best", labelcolor="linecolor")
plt.show()

#그림 6.3.8
x=np.linspace(-1, 3, 100)
f=x**2
plt.figure(figsize=(4,3))
plt.plot(x, f ,color="g", label=r"$f(x)=x^2$")
x1=np.linspace(0,2, 100)
f1=x1**2
plt.fill_between(x1, f1, color="r", alpha=0.3)
plt.hlines(4/3, (4/3)**0.5, 2, ls="--", color="b", label=r"$y_{avg}=\frac{4}{3}$")
plt.xlabel("x", fontsize=11)
plt.ylabel("y", rotation="horizontal",  fontsize=11)
plt.ylim(-0, 5)
plt.legend(loc="best", labelcolor="linecolor", frameon=False)
plt.show()

#그림 6.4.1
x0=np.linspace(-90, 360)
y0=np.sin(np.radians(x0))
fig, ax=plt.subplots(figsize=(4,3))
ax.plot(x0, y0 ,color="g", label="f(x)=sin(x)")
x=np.linspace(-90, 0, 30), np.linspace(0, 180, 30), np.linspace(180, 360, 30)
y=np.sin(np.radians(x))
col=["brown", "b","r"]
nme=["Aear1: -1.42", "Aear2: 1.99", "Aear3: 1.99"]
for i in range(len(x)):
    ax.fill_between(x[i], y[i], color=col[i], alpha=0.3, label=nme[i])
axisTran(ax)
ax.set_xlabel("x", loc="right",fontsize=11)
ax.set_ylabel("y", rotation="horizontal", loc="top", fontsize=11)
ax.set_xticks([-90,0, 90, 180, 270, 360], [r"$-\frac{\pi}{2}$", 0, r"$\frac{\pi}{2}$", r"$\pi$",r"$\frac{3\pi}{2}$", r"$2\pi$"])
ax.set_yticks([-1, -0.5, 0.5, 1])
ax.set_ylim((-1.1, 1.1))
ax.legend(loc="best", labelcolor=["g","brown", "b","r"])
plt.show()