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Math Help - double integrals!

  1. #1
    Junior Member
    Joined
    Oct 2008
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    69

    double integrals!

    hi guys, i have a question that im pretty sure im doing right but i keep gettin the wrong answer. it says:

    Find mass and Center of Mass for the following:
    Dis bounded by the parabola x = y^2 and the line y = x - 2 with density(x,y) = 3. for the mass, i did:

    m = (integral from x = 0 to x = 4)(integral from y = x-2 to y = x^(1/2) of 3 dydx

    I am getting m = 16, but my book says m = 27/2 = 13.5

    Could you help me find out what my mistake is??? Thank you in advance!
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  2. #2
    Senior Member
    Joined
    Apr 2009
    From
    Atlanta, GA
    Posts
    408

    Bounds of integration

    First, you have the wrong bounds of integration. Second, you are integrating with respect to x instead of y. Try drawing the two graphs on a piece of paper and look carefully at the situation.

    x_1=y^2, x_2=y+2 has intersection points (1,-1),(2,4). So the integral is A=\int_{-1}^2 y+2-y^2 dy. Multiplying this result by the constant density \rho=3 does indeed get you a correct answer.
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