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Calculus AB

posted by on .

y=6-x y=x^2

Find the area of the region by
integrating with respect to x.

Find the area of the region by integrating with respect to y.
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i got the intersection pts to be(-3,9)and (2,4)....i then took the integral and found the answer to be 20.8333 for both parts...HOWEVER...its wrong! please help!

  • Calculus AB - ,

    Your intersection points are correct
    Method1:
    the effective height of a slice = 6-x - x^2

    area = ∫ (6-x - x^2) dx from x = -3 to 2
    = [6x - x^2/2 - x^3/3] from -3 to 2
    = 12 - 2 - 8/3 - (-18 -9/2 - (-27/3) )
    = 10 - 8/3 + 9 + 9/2
    = 19 + 11/6
    = 20 5/6 or 125/6 , so you were right

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