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Math Help - A few problems

  1. #1
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    A few problems

    I have a few problems on a review for a test on Thursday morning that I am either just not getting or I am not sure if I am right.

    1) Find the arc length from (x1, y1) to (x2, y2) on the graph of f(x)=mx+b.

    I just don't see how you can find the arc length of a straight line.


    2) Find the volume formed by revolving the region bounded by the graphs of y=x^3+x+1, y=1, and x=1 about the line x=2 using the shell method.


    3) Find the center of mass of the region bounded by the graphs of f(x)=4-x^2 and g(x)=x+2


    4) A force of 750 pounds compresses a spring 3 inches from its natural length of 15 inches. Find the work done in compressing the spring an additional 3 inches.

    For this one I got a force of 4500 in-lb for the entire 6 inches being compressed, and when I integrated from 3 to 6 I got 3375 in-lb for the additional 3 inches. I am not sure if this is right or not.


    Thanks in advance for any help you can provide.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Zolthas View Post
    I have a few problems on a review for a test on Thursday morning that I am either just not getting or I am not sure if I am right.

    1) Find the arc length from (x1, y1) to (x2, y2) on the graph of f(x)=mx+b.

    I just don't see how you can find the arc length of a straight line.


    2) Find the volume formed by revolving the region bounded by the graphs of y=x^3+x+1, y=1, and x=1 about the line x=2 using the shell method.


    3) Find the center of mass of the region bounded by the graphs of f(x)=4-x^2 and g(x)=x+2


    4) A force of 750 pounds compresses a spring 3 inches from its natural length of 15 inches. Find the work done in compressing the spring an additional 3 inches.

    For this one I got a force of 4500 in-lb for the entire 6 inches being compressed, and when I integrated from 3 to 6 I got 3375 in-lb for the additional 3 inches. I am not sure if this is right or not.


    Thanks in advance for any help you can provide.
    f(x)=mx+b

    f'(x)=m

    \sqrt{1+f'(x)^2}=\sqrt{1+m^2}

    \int_{x_0}^{x_1}\sqrt{1+m^2}dx

    =\sqrt{1+m^2}x\bigg|_{x_0}^{x_1}=\sqrt{1+m^2}\left  (x_1-x_0\right)
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