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's differentiation thread. Many thanks to Hootenanny for reviewing it along with Dr. Transport 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.