This document discusses double integration in Cartesian form. It introduces double integration as integrating over a two-dimensional area using two variables, unlike single integration which uses one variable. An example of double integration is then provided to approximate the area under a 2D curve using two variables. The document also discusses the properties and rules of double integration that can help simplify functions and compute double integrals.

1. DOUBLE INTEGRATION IN CARTESIAN
FORM
BY:- PRIYANSHU KUMAR
MATHEMATICS -1
PROJECT

2. INTRODUCTION
Double integral is a type of integration in which the integration
is done using two variables over a defined region. Double
integral is a way to integrate over a two-dimensional area.
We use a single integral when we are approximating the area
using one variable only. But in Double Integral we use two
variables to approximate the area. This use of two variables
helps us to approximate components for higher dimensions
like area or volume under a 2D curve.
BY:- PRIYANSHU KUMAR

3. EXAMPLE
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4. Evaluation of Double Integral
Double and triple integrals were calculated way before the notion of
integral was formalized, since antiquity, by people like Archimedes and
Eudoxus, but for each particular integral a new argument was
invented. They approximated integrals by finite sums and then tried to
find the limit. The difficulty was in finding the limit explicitly. In the
17th century, Cavalier's Principle was formulated which helped in
evaluating some multiple integrals, especially for areas and volumes.
Modern calculus books prefer to refer to a very general Fubon
theorem, which is one we study at present.
BY:- PRIYANSHU KUMAR

5. The properties of Double Integral are very helpful when
computing them or otherwise working with them. They help to
simplify the given function. The properties of Double Integral
are listed below.
If we consider the functions f(x, y) and g(x, y) integrable
over the rectangular region R where S and T are subregions
of R and m and M are real numbers, then we can describe the
following properties.
Double Integral Properties
BY:- PRIYANSHU KUMAR

6. Double integral Rules
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7. Double Integral Solved Examples
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8. THANK YOU
BY:- PRIYANSHU KUMAR