Integration: Notes and Tips for Differentiation in Scientific Research?

[Kurdt]

The following PDF contains some notes I prepared and modified slightly for posting here. Its been modified to compliment Hootenanny[/color]'s differentiation thread. Many thanks to Hootenanny[/color] for reviewing it along with Dr. Transport[/color] and rbj and others.

As ever, any comments, corrections/suggestions can be directed to me by private message.

Corrections will be posted in this thread. Hopefully there won't be too many.

View attachment Intro to Integration 2.pdf

 

[Greg Bernhardt]

looks great Kurdt, thanks!

 

[cristo]

That's awesome.. good work Kurdt!

 

[Kurdt]

Just a note to remind users that this is an informal reference and shouldn't be used as a students only resource for learning.

 

[Big-T]

Shouldn't there be some absolute value signs in the section dealing with trigonometric substitution?

 

[cristo]

Shouldn't there be some absolute value signs in the section dealing with trigonometric substitution?

You'll need to be more specific than that!

 

[Big-T]

In the middle of page 8 (), it says that $$\sqrt{a^2\cos^2x}=a\cos x$$.

 

[Kurdt]

There should be an updated version coming soon with a few corrections.

 

[free4eternity]

Great work, Kurdt. THANKS!

 

[Sci.Jayme]

Thank you for this, I will read through it since this is my study level right now.
Is this something I can rely on though, as fully accurate?

 

[Kurdt]

Thank you for this, I will read through it since this is my study level right now.
Is this something I can rely on though, as fully accurate?

As I have said in a previous post, this is something that should not be used by itself by students. It is made to supplement textbooks and course notes as more of a quick reference guide. Some people have already pointed mistakes out and that's why I'm working on an updated version (when I get the time). If you spot any please post them in this thread.

 

[NoMoreExams]

You might also mention a more generalized version of FTC:

If $$F(x) \, = \, \int_{g(x)}^{h(x)} f(t) \, dt$$, then $$F'(x) \, = \, f(h(x))h'(x) \, - \, f(g(x))g'(x)$$

 

[JeffNYC]

Cool man - thanks for sharing this.