VMiP_2.1

# Lab2 variant 17
from cmath import exp
import matplotlib.pyplot as plt
import numpy as np

def F(x):
    """Возращает первообразную"""
    #result = x - np.log(np.exp(x) + 1)
    result = -(np.exp(x)/(np.exp(2 * x) + 2 * np.exp(x) + 1))
    return abs(result)

def f(x) -> float:
    return np.exp(-x)/(1+np.exp(-x))



fig, ax = plt.subplots()
x = np.linspace(0,np.pi,10)
y = np.exp(-x)/(1+np.exp(-x))
eps = 0.000001
a = 0
b = np.pi
ax = ax.plot(x, y, "b-")
ax = plt.gca()
ax.spines['left'].set_position("center")
ax.spines['bottom'].set_position('center')
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.set_xlabel("Y", fontsize=15, color='blue', labelpad=120)    # +
ax.set_ylabel("X", fontsize=15, color='orange', labelpad=140, rotation=0)
plt.show()
"""# кол-во разбиений
n = 100
# шаг
h = (b - a) / n
sum = 0
for i in range(1, n + 1):
    xi = a + i * h
    sum += f(xi)
sum = h * sum
print(f'Интеграл = {sum}')"""
# Найдем шаг разбиения
h1 = F(a)
h2 = F(b)
if h1 >= h2:
    max = h1
else:
    max = h2
#print('max = ', max)

n = 1
#print(max * ((b-a)**2)/(2*n))
while (max * ((b-a)**2)/(2*n) >= eps):
    n += 1
print(f'Количество разбиений при точности {eps}; n = {n}')
h = (b - a) / n
sum = 0
for i in range(1, n + 1):
    xi = a + i * h
    sum += f(xi)
sum = h * sum
print(f'Интеграл = {sum:.5f}')