#import "template.typ": *

// Take a look at the file `template.typ` in the file panel
// to customize this template and discover how it works.
#show: project.with(
  title: "Multiple Integrations",
  authors: (
    "<NAME>",
  ),
  date: "30 Octobre, 2023",
)

#set heading(numbering: "1.1.")

= Multiple Integrations
<multiple-integrations>
== Definition
<definition>
Multiple integrals are a way of extending the concept of a single
integral to integrate functions with more than one variable. In other
words, a multiple integral is a mathematical operation that calculates
the integral of a function with multiple variables, such as a function
of two variables (x and y) or a function of three variables (x, y, and
z). These integrals can be used to solve a variety of problems in
mathematics and other fields, such as finding the volume of a
three-dimensional object or calculating the amount of force acting on a
surface. The general form of a multiple integral is:
`∫∫ f(x, y, z) dx dy dz`

where f(x, y, z) is the function being integrated, and dx, dy, and dz
are the differentials of the variables x, y, and z, respectively. The
process of evaluating a multiple integral involves breaking the region
over which the integral is being calculated into many small subregions
and calculating the integral over each subregion. This can be a complex
process, but there are many tools and techniques that can be used to
make it easier.
