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Math Help - Area from a definite integral

  1. #1
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    Area from a definite integral

    I am suppose to obtain an area bound by 3x + y = 6 above and below by y = x^2 - 4 and the y axis. I think I should take the integral of the first and subtract the integral of the second one from 0 to 2

    In terms of x: 6x - 3x^2/2 - (x^3/3 + 4x) from x = 0 to 2. Am I on the right track on this one????? Please let me know. I asked someone else in my class and they added the two integrals and used |x^2 - 4| for second integral?? Thanks again for this wonderful site!!!! Frost King
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  2. #2
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    to find the area between the line and the curve, first find where the line and the curve intersect.

    y = 6 - 3x

    y = x^2 - 4

    x^2 - 4 = 6 - 3x<br />

    x^2 + 3x - 10 = 0

    (x + 5)(x - 2) = 0

    x = -5 , x = 2

    A = \int_{-5}^2 (6-3x) - (x^2 - 4) \, dx

    simplify the integrand, integrate, and use the FTC.
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