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Math Help - areas bounded by curves

  1. #1
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    areas bounded by curves

    I have to find the area of the area bound by y^2=4x and y=2x-4

    I have to find the points of intersection. would I do this by solving 2x-4 = 4x or by 2x-4 = sqrt(4x) or both?
    Last edited by colorado; May 31st 2011 at 09:41 AM. Reason: i realized bounded isn't proper, lol
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  2. #2
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    No, y is not equal to y^2! You can write y= sqrt(4x)= 2sqrt(x) and set that equal to 2x- 4. But it might be simpler to write x= y^2/4 so that y= 2(y^2/4)- 4= y^2/2- 4 and solve that quadratic equation.
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  3. #3
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    im slightly confused by the response. what would a, b ,and c be then for the quadratic equation. well c = -4, but what would a and b be?
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  4. #4
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    I keep getting x=4, but there should be another one that is x=-2 according to the back of the book. because the interval is -2<x<4
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  5. #5
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    Quote Originally Posted by colorado View Post
    I keep getting x=4, but there should be another one that is x=-2 according to the back of the book. because the interval is -2<x<4
    No. This is the integral \int_{ - 2}^4 {\left( {\frac{{y + 4}}{2} - \frac{{y^2 }}{4}} \right)dy} .
    Because the two curves meet at (1,-2)~\&~(4,4).
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  6. #6
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    now I am confused more. one of those days. how are you getting the intersection points, and I still don't see how i can get a quadratic equation out of this
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  7. #7
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    Quote Originally Posted by colorado View Post
    now I am confused more. one of those days. how are you getting the intersection points, and I still don't see how i can get a quadratic equation out of this
    Just solve (2x-4)^2=4x.
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  8. #8
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    and there it is, thank you
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