integration in python symbolic and numeric

integration is a fundamental concept in calculus, and it can be performed in python using both symbolic and numeric methods. in this tutorial, we'll cover both approaches using popular libraries: `sympy` for symbolic integration and `scipy` for numeric integration.

1. symbolic integration using sympy

**sympy** is a python library for symbolic mathematics. it allows you to perform algebraic manipulations, calculus, and more.

installation

to use sympy, you need to install it. you can do this via pip:

example of symbolic integration

here's how to perform symbolic integration using sympy:

explanation:
- we import the `sympy` library.
- we define `x` as a symbol.
- we define the function `f` to integrate, in this case, `sin(x)`.
- we use the `integrate` function to compute the integral with respect to `x`.
- the result is displayed, and we add `+ c` to indicate the constant of integration.

2. numeric integration using scipy

**scipy** is a scientific computing library in python that provides tools for numeric integration, among other things.

installation

to use scipy, you also need to install it:

example of numeric integration

here's how to perform numeric integration using scipy:

explanation:
- we define the function `integrand`, which is `sin(x)` in this case.
- we set the limits of integration, `a` (0) and `b` (π).
- we call `quad` to perform the numeric integration, which returns the result and an estimate of the error.
- finally, we print the result and the estimated error.

summary

in this tutorial, we covered:

1. **symbolic integration** using sympy:
- how to define symbols and functions.
- how to perform integration and interpret the results.

2. **numeric integration** using scipy:
- how to define a function for numeric integration.
- how to specify integration limits and obtain results along with error estimates.

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integration
Python
symbolic integration
numeric integration
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numerical methods
definite integral
indefinite integral
calculus
mathematical functions
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integration techniques