viichi

from math import cos, sin, pi
from scipy import integrate
import numpy as np


def f(x):
    return x * cos(x) ** 2


def df(x):
    return -2 * x * sin(x) * cos(x) + cos(x) ** 2


a = 0
b = pi / 2
s = 0

# Задание №1 Пункты №1-3

# J = integrate.quad(f, a, b)
#
# print(f"J = {J}\n")
#
# for k in range(1, 16):
#     s = 0
#     x0 = a
#     n = 10 ** k
#     h = (b - a)/n
#     for i in range(n):
#         s += f(a + i * h)
#     s *= h
#     print(f"{k:d}            |  {s:.15f}   |    {abs(J[0] - s)}")

# Задание №1 Пункты №4-6

# print(f"Производная заданной функции: -2*x*sin(x)*cos(x) + cos(x)**2\n")
# dif = df(a)
# print(f"D = df(a) = {dif}\n")
#
# for k in range(1, 16):
#     h = (b - a)/(10 ** k)
#     x0 = a + h
#     s = (f(x0 + h) - f(x0 - h)) / 2 / h
#     print(f"{k:d}            |  {s:.15f}  |   {abs(dif - s)}")