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Math Help - A smart way to avoid a lot of Inverse hassle?

  1. #1
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    May 2010
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    A smart way to avoid a lot of Inverse hassle?

    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,

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

    siny = 2x^2

    cosy \cdot \frac{dy}{dx} = 4x

    \frac{dy}{dx} = \frac{4x}{cosy}

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

    \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?
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  2. #2
    Junior Member allsmiles's Avatar
    Joined
    May 2010
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    Altlanta GA
    Posts
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    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 hereCalculus 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
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  3. #3
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    Joined
    May 2010
    Posts
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    Quote Originally Posted by allsmiles View Post
    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 hereCalculus 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

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

    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!
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