# Integration lessons

Status
Not open for further replies.

#### ZaidAlyafey

##### Well-known member
MHB Math Helper
Hello MHB members , I am thinking about starting some lessons on Integration techniques
I will basically introduce some integration techniques from the very simple to the complicated ones on this site , so I was wondering whether it is a good idea ?

#### MarkFL

Staff member
That's a wonderful idea. You should post them in the Math Notes sub-forum along with our other tutorials.

Go to the Useful Mathematics Resources sub-forum, and there you will find a sub-forum titled Math Notes.

#### chisigma

##### Well-known member
Hello MHB members , I am thinking about starting some lessons on Integration techniques
I will basically introduce some integration techniques from the very simple to the complicated ones on this site , so I was wondering whether it is a good idea ?
Good idea!... because the field is very wide, only one clarification: what You mean as 'integration techniques'?... general concept of integral?... indefinite integrals?... exact computation of definite integrals?... numerical computation of definite integrals?...

Kind regards

$\chi$ $\sigma$

#### Ackbach

##### Indicium Physicus
Staff member
Hello MHB members , I am thinking about starting some lessons on Integration techniques
I will basically introduce some integration techniques from the very simple to the complicated ones on this site , so I was wondering whether it is a good idea ?
I have started a tutorial in the Calculus folder on integral calculus. I need to finish it, but haven't the time right now. You might check that out, if you like, and either continue it, or you could do some more advanced techniques. What's your scope?

#### ZaidAlyafey

##### Well-known member
MHB Math Helper
Good idea!... because the field is very wide, only one clarification: what You mean as 'integration techniques'?... general concept of integral?... indefinite integrals?... exact computation of definite integrals?... numerical computation of definite integrals?...

Kind regards

$\chi$ $\sigma$
Hi chisigma thanks for your reply .

I will try to tackle the several techniques to solve definite and indefinite integrals because as we know many indefinite integrals cannot be solved but if we define them in a bounded interval they can be solved .
These techniques will include the elementary ones [By substitution , by parts , by partial fractions ,etc...] . In addition to complicated ones , such as [The use of special functions ,using Laplace and Rourier transform , Complex and contour Integration ,etc...].
Basically , there will be lots of exercises and proofs of general formulas.

#### ZaidAlyafey

##### Well-known member
MHB Math Helper
I have started a tutorial in the Calculus folder on integral calculus. I need to finish it, but haven't the time right now. You might check that out, if you like, and either continue it, or you could do some more advanced techniques. What's your scope?
Hi Ackbach thanks for the reply .

Oh , that is really nice you are introducing the concept which is extremely beneficial . On my part I will try to give so many exercises on solving integrals so students know how to tackle different problems. I see that you are more expert in explaining things , possibly a current teacher or so. Maybe you are planning that your tutorials will go in a certain pace or order so that students will be able to follow you. I don't think it is a good idea for me to continue your tutorial.

#### Ackbach

##### Indicium Physicus
Staff member
Hi Ackbach thanks for the reply .

Oh , that is really nice you are introducing the concept which is extremely beneficial . On my part I will try to give so many exercises on solving integrals so students know how to tackle different problems. I see that you are more expert in explaining things , possibly a current teacher or so. Maybe you are planning that your tutorials will go in a certain pace or order so that students will be able to follow you. I don't think it is a good idea for me to continue your tutorial.
Then why don't you focus on the more advanced techniques? I was not planning on going there, but was more planning on following a traditional Calculus II outline - so I would cover by-parts, substitutions, trig substitutions, and maybe one or two other methods, as well as the typical applications like force on a dam, volumes of solids of revolution, volumes of other kinds of solids, area between curves, etc. Chris L T521 is planning on doing a DE's tutorial, so I was going to leave that out.

By the way, I am currently a teacher of mathematics and physics at a high school in Texas. Hence my little title "doctor physicorum", which means "teacher of natural philosophy" in Latin.

I'll tell you one thing I'd love to see: a tutorial on differentiation under the integral sign. That technique requires a simply enormous amount of imagination to "see the trick", and anything that can make this very powerful trick available to mere mortals such as myself would be greatly appreciated.

#### Deveno

##### Well-known member
MHB Math Scholar
More stuff I think would be nice to see covered (in no particular order):

"term-by-term" integration (using power series, when you can, when you can't)
Hyperbolic functions
Fubini's theorem (including counter-examples where it doesn't work)
Arc-length
Arc-length paramaterization
Surface integrals
Green's Theorem

i like the idea of seeing "special functions" used. am looking forward to it.

#### ZaidAlyafey

##### Well-known member
MHB Math Helper
Ok, then I will focus on advanced techniques of integrations :

Here is a list with no particular order

-Using Differentiation under the integral sign .
-Using hyperbolic functions .
-Using series.
-Using transforms [Laplace , Fourier].
-Using special functions [gamma, beta ,digamma ... ]
-Contour integrations [Jordan's Lemma , indented contour , multi valued functions solutions , ... ]

I guess that is all ...

#### MarkFL

Staff member
I look forward to your tutorial, and I will probably have questions as I could certainly stand to learn some more advanced integrating techniques!

#### ZaidAlyafey

##### Well-known member
MHB Math Helper
I look forward to your tutorial, and I will probably have questions as I could certainly stand to learn some more advanced integrating techniques!
Oh that puts a great load on my back , I hope I will be up to that .