Double Integration.

WORK IN PROGRESS

Let’s start the blog with the definition of a Double integration and some examples.

An Integral is defined as the sum of all the infinitely small diferentials of the surface/area... or as the area of the region in the xy-plane bounded by the function F and the x-axis. It may also be referred as the "Antiderivative" due to the fact that is the opposite of a Derivate.

In the case of the double integral, the double integral of a positive function of two variables (x and y; Ro and Theta) represents the volume of the region between the surface defined by the function (on the three dimensional Cartesian plane where z = f(x, y) and the plane which contains its domain. 

The result of a double Integral is obtained in a similar way of the Definite Integral, but following some steps. First you have to decide which of your two variables is going to be the Main Variable, and which is going to be the Auxiliary Variable. Once you have done this, you have to integrate first the Auxiliary variable, treating the other variable as a constant, and then, once you have applied the values to the integrated function, you integrate a second time with the Main variable and apply its values.

Lets see an example so we can see it more visually.

Function F(x,y)= xy^2

In a double integral, the outer limits must be constant, but the inner limits can depend on the outer variable. This means, we must put y (the Auxiliary variable) as the inner integration variable, as shown in the following image:

There are many ways to solve a Double Integral, depending on which Geometrical Figure we are dealing with and in with plane (Cartesian, Polar or Bipolar) this figure is, but we will always solve this integrals using this same method, but changing the variables for each coordinate change.

Hope you have enjoyed this post and Hope to receive some feedback on what I can improve.

Here I will leave you some links so you can learn more about Double Integration.

Paul´s Online Math Notes

Video: Calculating a Double Integral.   

(Best of all Youtube Videos even though is on moodle)

I DO HAVE TO CHANGE THIS POST IN ORDER TO MAKE ALL THE BLOG ABOUT THE SAME SUBJECT.

Blog Presentation.

Welcome to my Blog.

This Blog has been created by Miguel Cervero Fernandez as an integrated proyect for the 1st year of Mechanical Engineer Degree taught at the Polytechnic School of the "Universidad Europea de Madrid". Academic Year 2013-2014.

My name is Miguel Cervero, I am a first year student of the course Mechanical Engineer in the Polythecnic School of the "Universidad Europea de Madrid".
This is a class project in which we will discuss many matters related to Calculus and Algebra . The main objective of this blog is to help students learn about the practical uses of Calculus and Algebra in their first year of Mechanical Engineer.
I have the intention to post different exercises and articles to be able to fully understand how Math is related to the world.
I hope that when i finish this blog at the end of the year we will all have learned a little bit more about Calculus, Algebra and Blogger :D.

As a first piece of information here you have a link to a great internet mathematical tool, the Cientific Calculator: Wolfram-Alfa.
http://www.wolframalpha.com/.