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Math Help - parabola trouble!

  1. #1
    Newbie
    Joined
    Feb 2010
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    parabola trouble!

    hey totally stuck on this problem!
    Find the area of the region that is enclosed by the horizontal line y=3 and the parabola y=x^2-1?

    help would be mucho appreciated!
    (don't know how to put in squared..new to this!)
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  2. #2
    Senior Member
    Joined
    Jan 2010
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    First, look at the graph:



    Identify the endpoints of the region (I'll call them a and b) and which curve is "above" and which is "below". (I'll call them T(x) for top and B(x) for bottom.)

    Then we set up the integral:

    \int_a^b \left[T(x) - B(x)\right] dx = \int_{-2}^2 \left[3 - (x^2-1)\right] dx =  \int_{-2}^2 (4 - x^2) \, dx

    Do you know how to solve this?
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  3. #3
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    Feb 2010
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    Unhappy eek!

    nope not really..im really struggling with this..it just doesnt seem to be sinking in!
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  4. #4
    MHF Contributor

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    Where exactly is your problem? Are you saying you do not know how to integrate 4- x^2? Do you not know that the integral of x^n is \frac{1}{n+1}x^{n+1}+ a constant?
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