from sympy import *
init_printing(use_latex='mathjax')
n, m = symbols('n,m', integer=True)
x, y, z = symbols('x,y,z')
In the last section we learned symbolic differentiation with .diff
. Here we'll cover symbolic integration with integrate
.
Here is how we write the indefinite integral
$$ \int x^2 dx = \frac{x^3}{3}$$# Indefinite integral
integrate(x**2, x)
And the definite integral
$$ \int_0^3 x^2 dx = \left.\frac{x^3}{3} \right|_0^3 = \frac{3^3}{3} - \frac{0^3}{3} = 9 $$# Definite integral
integrate(x**2, (x, 0, 3))
As always, because we're using symbolics, we could use a symbol whenever we previously used a number
$$ \int_y^z x^n dx $$integrate(x**n, (x, y, z))
Compute the following integrals:
$$ \int \sin(x) dx $$$$ \int_0^{\pi} \sin(x) dx $$$$ \int_0^y x^5 + 12x^3 - 2x + 1 $$$$ \int e^{\frac{(x - \mu)^2}{\sigma^2}} $$Feel free to play with various parameters and settings and see how the results change.
# Use `integrate` to solve the integrals above
Are there some integrals that SymPy can't do? Find some.
# Use `integrate` on other equations. Symbolic integration has it limits, find them.