A smart way to avoid a lot of Inverse hassle?

May 2010
16
0
Hi, Calculus is about logic & it's great because
if you figure out the underlay of specific things
you can sidestep memorizing a heckload of
information.

To me the only hard thing is finding these tricks,
I'm specifically having a problem with integrating
inverse trigonometric functions.

For taking the derivative it's simple,

\(\displaystyle y = sin^{-1}(2x^2)\)

\(\displaystyle siny = 2x^2\)

\(\displaystyle cosy \cdot \frac{dy}{dx} = 4x\)

\(\displaystyle \frac{dy}{dx} = \frac{4x}{cosy}\)

\(\displaystyle \frac{dy}{dx} = \frac{4x}{\sqrt{1 - sin^2y} }\)

\(\displaystyle \frac{dy}{dx} = \frac{4x}{\sqrt{1 - 4x^4} }\)

and voila!

No memorizing whatever it is that litters up
the engineering book I foolishly bought.

However, for integrating these functions I don't see
the easy process.

Like, there are 6 functions all differing very slightly
and there's no way I'll be able to memorise them.
Every source I've checked tells me that because I know
the derivatives I can just reverse the process & copy
the form & write the integral. Yay!

Except, I'd have to go through up to a possible 6 side
calculations of derivatives to search out which
form my current integral is in so I can just magially
copy it.

Is there no better way than rote memorization?

Is there no simple logical model to follow that
generalizes to all 6 functions like taking derivatives
of them all has?
 
May 2010
53
1
Altlanta GA
LoL, i found your comments very funny, but unless you buy a book, or look it up on the internet, i think the way you are doing it is the best way to do it, without messing up.

you could always look here:)Calculus Primer Calculus Tutorial

i looked at it and i thought it was so stupid, who knows, you may be a lucky person, unlike my. Lol :)
 
May 2010
16
0
LoL, i found your comments very funny, but unless you buy a book, or look it up on the internet, i think the way you are doing it is the best way to do it, without messing up.

you could always look here:)Calculus Primer Calculus Tutorial

i looked at it and i thought it was so stupid, who knows, you may be a lucky person, unlike my. Lol :)
Lol thanks (Rofl)

That calculus primer tutorial looks more complicated than my lazy book! (Wondering)

If your having trouble with calc & have resorted to using that scary looking calculus primer site I found a huge list of links in some post on this site that you might like, I think they are great!

UCCS | Department of Mathematics (requires registration but is free)
http://www.sci.uidaho.edu/polya/math...=1&sec=1&sub=0
Free downloadable Maths Video Lecture courses
http://www.math.ncsu.edu/calculus/we...1lectures.html
http://courses.ncsu.edu/ma107/common...7Lectures.html
http://webcast.berkeley.edu/course_d...sid=1906978460
Khan Academy
Just Math Tutoring
Calculus-Help.com: Survive calculus class! - Tutorials for the Calculus Phobe
Find thinkwell Videos at 5min.com

The guy in the videos of the last one is great, so is the guy khan, and the first link is like real college classes videotaped!

They don't really help me with my problem lol but they are good for a lot of other things I found!(Cool)