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Math Help - Definite Integrals

  1. #1
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    Definite Integrals

    explain whe the function f(x) = x2 - 4/x-2 is not continuous on [0,3] what kind of discontinuity occurs?
    use areas to show that integral 0,3 x2-4/x-2 dx = 10.5
    use areas to show that integral 0,5 int(x) dx = 10.

    how do i do these i really need some help on this my math teacher dosen't really teach.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by dblader View Post
    explain whe the function f(x) = x2 - 4/x-2 is not continuous on [0,3] what kind of discontinuity occurs?
    use areas to show that integral 0,3 x2-4/x-2 dx = 10.5
    use areas to show that integral 0,5 int(x) dx = 10.

    how do i do these i really need some help on this my math teacher dosen't really teach.
    Have you graphed this? On the surface it looks like there might be a vertical asymptote at x = 2, but there is not:
    f(x) = \frac{x^2 - 4}{x - 2} = x + 2;~x \neq 2

    This has the aspects of a "hole" in the function.

    (By the way, please learn to use parentheses in your expressions. The function "x^2 - 4/x - 2" is really:
    f(x) = x^2 - \frac{4}{x} - 2
    and I know that this isn't what you meant.)

    -Dan
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    how do you do that like put in the equations

    sorry see what you mean about the equation how would i do this and show areas im pretty sure the type of discontinuity is a removable discontinuity but how do i use areas to shw that the last 2 equal that.

    \int_{0}^{3} \frac{x^2-4}{x-2}, dx = 10.5

    \int_{0}^{5} int(x), dx = 10
    Last edited by dblader; March 19th 2008 at 09:35 PM.
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  4. #4
    Behold, the power of SARDINES!
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    La Tex

    Quote Originally Posted by dblader View Post
    how do you do that like put in the equations

    Here is a link Helpisplaying a formula - Wikipedia, the free encyclopedia

    good luck.
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by dblader View Post
    how do you do that like put in the equations

    sorry see what you mean about the equation how would i do this and show areas im pretty sure the type of discontinuity is a removable discontinuity but how do i use areas to shw that the last 2 equal that.

    \int_{0}^{3} \frac{x^2-4}{x-2}, dx = 10.5

    \int_{0}^{5} int(x), dx = 10
    Except for x = 2 the function is nothing more than a line. So the integrals are merely triangles. You can use the area of a triangle to calculate the integrals. That is what the problem wants you to do.

    -Dan
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