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Math Help - Work-Related Integration Problem

  1. #1
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    Work-Related Integration Problem

    [SOLVED]

    I've been having trouble with this one. Help appreciated

    A carpet which is 7 meters long is completely rolled up. When x meters have been unrolled, the force required to unroll it further is

    F(x)=900/(x+2)^3 Newtons.

    How much work is done unrolling the entire carpet? Your answer must include the correct units.
    Last edited by Kimmy2; October 24th 2009 at 01:44 PM. Reason: Solved
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  2. #2
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    Quote Originally Posted by Kimmy2 View Post
    I've been having trouble with this one. Help appreciated

    A carpet which is 7 meters long is completely rolled up. When x meters have been unrolled, the force required to unroll it further is

    F(x)=900/(x+2)^3 Newtons.

    How much work is done unrolling the entire carpet? Your answer must include the correct units.
    W = \int_{x_1}^{x_2} F(x) \, dx

    W = \int_0^7 \frac{900}{(x+2)^3} \, dx

    units of work are Newton-meters = Joules
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  3. #3
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    I tried integrating using that method. I got -1/162.
    According to the website I get my homework from, it recorded that answer as incorrect. Did I integrate incorrectly?

    Am I supposed to use f(x)=kx, W=Fd, F=ma, somehow?
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  4. #4
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    Quote Originally Posted by Kimmy2 View Post
    I tried integrating using that method. I got -1/162.
    According to the website I get my homework from, it recorded that answer as incorrect. Did I integrate incorrectly?

    Am I supposed to use f(x)=kx, W=Fd, F=ma, somehow?
    I can tell you that the answer you have for the integral is incorrect. What did you get for your anti-derivative?
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  5. #5
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    I got (-450/x^2+4x+4).
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    Behold, the power of SARDINES!
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    Quote Originally Posted by Kimmy2 View Post
    I got (-450/x^2+4x+4).
    you need to integrate

    \int_{0}^{7}\frac{900}{(x+2)^3}dx

    Try a u-sub with u=x+2 \implies du=dx


    See if you can get it from here.
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  7. #7
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    Quote Originally Posted by Kimmy2 View Post
    I got (-450/x^2+4x+4).
    \left[-\frac{450}{(x+2)^2}\right]_0^7 = \frac{1925}{18}
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  8. #8
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    Woah. Thanks, Skeeter! That answer was correct. I wonder what I did wrong
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  9. #9
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    Quote Originally Posted by Kimmy2 View Post
    Woah. Thanks, Skeeter! That answer was correct. I wonder what I did wrong
    I don't know ... you didn't show your work.
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