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Math Help - Integration - Dr. Evil is my teacher

  1. #1
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    Integration - Dr. Evil is my teacher

    Right I won't bore you with a sob story but this is a regular grade 12 class and we've been posed with this problem:

    Find the arc length of this function across 0 -> 5:

    s(t) = t^3 - 6t^2 + 9t + 5, {t >= 0}

    I learned the formula of s = Integral of squareroot(1+f'(x)^2) * dx

    So I began using the Riemann sums until I get here, I'm not quite sure how to proceed.



    If need be I will show how I got up to there, it just takes forever to use LaTeX.

    PS: That should be x->infinity

    Thanks!
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  2. #2
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    Quote Originally Posted by Silent Soliloquy View Post
    Right I won't bore you with a sob story but this is a regular grade 12 class and we've been posed with this problem:

    Find the arc length of this function across 0 -> 5:

    s(t) = t^3 - 6t^2 + 9t + 5, {t >= 0}

    I learned the formula of s = Integral of squareroot(1+f'(x)^2) * dx

    So I began using the Riemann sums until I get here, I'm not quite sure how to proceed.



    If need be I will show how I got up to there, it just takes forever to use LaTeX.

    PS: That should be x->infinity

    Thanks!
    I don't see why you're trying to calculate the limit of the Riemann sum when you have the formula. That will be difficult. Why don't you just use the formula?
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  3. #3
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    Quote Originally Posted by adkinsjr View Post
    I don't see why you're trying to calculate the limit of the Riemann sum when you have the formula. That will be difficult. Why don't you just use the formula?
    Hm, I thought the Reimann sum was a way to find the integral. Oddly enough we never did integrals so I had to scour what I could from textbooks and the internet.

    Is the integral

    \frac{2}{3} (x+3(x^{2}-4x+3)^3)^\frac{3}{2}

    for the function

    (1+9(x^{2}-4x+3)^2)^\frac{1}{2}

    Thanks, sorry about all the trivial trouble.
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  4. #4
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    Quote Originally Posted by Silent Soliloquy View Post
    Hm, I thought the Reimann sum was a way to find the integral. It is one way, but they can be very difficult to evaluate. It's much like using the first principles to find a derivative. You can use the limit formula if you want, but it's just not something people often do since it just makes it too difficult. However, in your case it's really difficult to use the formula too.Oddly enough we never did integrals so I had to scour what I could from textbooks and the internet. That's pretty wierd, this topic isn't discussed until page 563 of my University Calculus text book. I think this is a Calc II topic.

    Is the integral

    \frac{2}{3} (x+3(x^{2}-4x+3)^3)^\frac{3}{2}

    for the function

    (1+9(x^{2}-4x+3)^2)^\frac{1}{2}

    Thanks, sorry about all the trivial trouble.
    No, this integral seems difficult to solve. I will start a new thread to see if anyone else can help. I'm afraid people may ignore your post since I responded to it. The integral you have to evaluate looks like this:

    \int_0^5\sqrt{1+(3t^2-12t+9)^2}dt

    I'm not sure if this is something that is practical to solve by hand. I will start a thread with this integral to see what
    others say.

    Thread: http://www.mathhelpforum.com/math-he...-integral.html
    Last edited by adkinsjr; November 9th 2009 at 01:51 PM.
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  5. #5
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    Quote Originally Posted by adkinsjr View Post
    No, this integral seems difficult to solve. I will start a new thread to see if anyone else can help. I'm afraid people may ignore your post since I responded to it. The integral you have to evaluate looks like this:

    \int_0^5\sqrt{1+(3t^2-12t+9)^2}dt

    I'm not sure if this is something that is practical to solve by hand. I will start a thread with this integral to see what
    others say.

    Thread: http://www.mathhelpforum.com/math-he...-integral.html
    I believe the integral is
    Last edited by Silent Soliloquy; November 9th 2009 at 02:20 PM.
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