sympy_symbolic_math_differentiation_integration_limits_quickstart.py

1from sympy import init_printing, Symbol, exp, diff, integrate, limit, sin, oo
2
3# Initialize pretty printing for better output readability
4init_printing(use_unicode=True)
5
6# Define a symbolic variable
7x = Symbol('x')
8
9# Perform a symbolic differentiation
10# Example: Derivative of e^x * sin(x)
11derivative = diff(exp(x) * sin(x), x)
12print(f"Derivative: {derivative}")
13
14# Perform a symbolic integration
15# Example: Indefinite integral of e^x * sin(x) + e^x * cos(x)
16integral = integrate(exp(x)*sin(x) + exp(x)*cos(x), x)
17print(f"Integral: {integral}")
18
19# Calculate a definite integral from -infinity to infinity
20# Example: Integral of sin(x^2) from -oo to oo
21def_integral = integrate(sin(x**2), (x, -oo, oo))
22print(f"Definite Integral: {def_integral}")
23
24# Calculate a limit
25# Example: limit of sin(x)/x as x approaches 0
26lim = limit(sin(x)/x, x, 0)
27print(f"Limit: {lim}")