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Math Help - area between the functions

  1. #1
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    area between the functions

    find the area between y = x^3 + 4x and y = 5x^2

    i basically drew out the diagram and the diagrams meet when x is 1 and zero.
    how do i find the area now? and from what intervals. i would need to calculate a total area then minus it from the total or sumthing ? thank u
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  2. #2
    Junior Member toraj58's Avatar
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    Lightbulb

    the digrams meets in 0, 1 and 4

    5x^2 - x^3 - 4x = 0 then answers for x are: 0,1 and 4

    now we can calculate the integral berween intervals.

    s = \int_{0}^{1} \left(f(x) - g(x)\right) + \int_{1}^{4} \left(f(x) - g(x)\right)
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  3. #3
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    Quote Originally Posted by toraj58 View Post
    the digrams meets in 0, 1 and 4

    5x^2 - x^3 - 4x = 0 then answers for x are: 0,1 and 4

    now we can calculate the integral berween intervals.

    s = \int_{0}^{1} \left(f(x) - g(x)\right) + \int_{1}^{4} \left(f(x) - g(x)\right)
    so i integrate s = \int_{0}^{1} x^3 -5x^2+4x  dx + \int_{1}^{4} x^3 -5x^2+4x  dx yeah ?

    my answer was -32/3.
    Last edited by jvignacio; November 12th 2008 at 08:13 AM.
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  4. #4
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    Before setting up those integrals, one has to check that f(x)-g(x) is positive or negative on [0,1], in the same fashion check that f(x)-g(x) is positive or negative on [1,4]. After concluding that, set up the integrals.
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  5. #5
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    Quote Originally Posted by Krizalid View Post
    Before setting up those integrals, one has to check that f(x)-g(x) is positive or negative on [0,1], in the same fashion check that f(x)-g(x) is positive or negative on [1,4]. After concluding that, set up the integrals.
    i understand.. is my result correct ?
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  6. #6
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    It can't be correct, the result should be positive.
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  7. #7
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    Quote Originally Posted by Krizalid View Post
    It can't be correct, the result should be positive.
    so what happens with one of them is negative? the f(x)-g(x)?

    my answer is now 71/6 when i get the magnitute of the 2nd integration
    Last edited by jvignacio; November 12th 2008 at 01:22 PM.
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  8. #8
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    Quote Originally Posted by toraj58 View Post
    the digrams meets in 0, 1 and 4

    5x^2 - x^3 - 4x = 0 then answers for x are: 0,1 and 4

    now we can calculate the integral berween intervals.

    s = \int_{0}^{1} \left(f(x) - g(x)\right) \, {\color{red}dx} + \int_{1}^{4} \left({\color{red}g(x) - f(x)}\right) \, {\color{red}dx}
    Corrections in red.

    To the OP of the thread (NOT the quoted post): You should realise which curve is f(x) and whch curve is g(x). It's always strongly advised to draw the graphs. Did you?
    Last edited by mr fantastic; November 12th 2008 at 01:31 PM. Reason: Clarifying which OP I meant
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  9. #9
    Junior Member toraj58's Avatar
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    no, i did not....i gave him the clue....he should do...thanks
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  10. #10
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    Quote Originally Posted by toraj58 View Post
    no, i did not....i gave him the clue....he should do...thanks
    Sorry, I should have been clearer which OP I meant. I didn't mean you lol!
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  11. #11
    Junior Member toraj58's Avatar
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    okay; thanks for making clear for him.
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