Informatics_and_prog_3.2

from cmath import asin
import math
import matplotlib.pyplot as plt
import numpy as np
import sympy as sym
from sympy.stats import Arcsin
from scipy.optimize import minimize, minimize_scalar, fmin
from sympy.sets import *
from sympy.calculus.util import continuous_domain
from sympy import Symbol, limit, S
from sympy.functions import asin



def f(x) -> float:
    """Функция"""
    return ((x**2/2)-1)


# Постройка графика
fig, ax = plt.subplots()
x = np.linspace(-10,10,50)
# функция f(x) = x^2/2-1
y = ((x**2/2)-1)
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.title(r'функция $y = x^2$/2-1')

z = Symbol('z')
# найдем точки пересечения с осью Ox
roots = sym.solve((z**2/2)-1)

print(f'Верхний предел = {roots[1]}\nНижний предел = {roots[0]}')
# производная
derivative = sym.diff((z**2/2)-1)

a = roots[0]
b = roots[1]

# (1+derivative**2)**(1/2)
# Нахождение длины дуги по форумле integral(a,b) sqrt(1+derivate^2) dx
# https://mathforyou.net/online/calculus/arclen/cartesian/
# Дока по интегралам https://docs.sympy.org/latest/modules/integrals/integrals.html
length = sym.integrate(sym.sqrt(1+derivative**2), (z, a, b))
print(f'Длина дуги = {length}')

#plt.fill_between(x, y, where = (y >= -1) & (x <= np.sqrt(2)) & (x >= -np.sqrt(2)),color='cyan')

plt.show()