Integration

Often called the anti-derivative, integration is the opposite act of differentiation. Instead of finding the rate of change of a function you instead are finding the area under the graph of this function.

The function being integrated ( in the example above) is called the integrand.

Much like differentiation you can apply a set of rules to a function to integrate it, these rules are given in diff-rules.

When finding the integral of a function a constant of integration must be used to account for unknown data about the original function, namely it's starting conditions.

For finding integrals of multiple variables see multiple integrals.

Solving

#incomplete

There are multiple ways to approximate the solution of an integral namely the midpoint-rule, trapezoidal-rule and the more accurate simpsons-rules.

One can use u-substitution to get their integral into one of the forms defined in the integration rules.

Solving using Python

(Using the SymPy Online Interpreter) You can find integrals using SymPy's integrate function. Given a function to integrate:

The integrate function takes multiple inputs: the function to integrate and the bounds of integration. It uses this syntax: integrate(f(x), (x, lower bound, uppper bound))

integrate(sqrt(x), (x, 0, 1))

add indefinite integrals