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Math Help - Graph the area bounded by....

  1. #1
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    Graph the area bounded by....

    graph the area bounded by y= x^2 +1 and y= -x +3

    find the volume of the solid formed by revolving teh area bout the x-axis

    h=____?

    DISC or washer method?

    find all the radiuses

    use integration to find the volume...


    i was trying this problem and.. i gotten

    AREA= pi r ^2

    v= intergral from a to b A dx

    two intergrals.. 0 to -2.. and 0 to 1

    PI( R^2 Outer - r^2 in)

    i had some help from a friend but im still utterly confused and i have my finals tommorow...

    i really need help from you guys.. thanks alot! willing to be pressing alot of thank buttons tonight ;P
    Last edited by CalculusDUMMIE; June 4th 2009 at 08:26 PM. Reason: major typo with X/Y values
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by CalculusDUMMIE View Post
    graph the area bounded by x = y^2 + 1 and x = -x +3

    find the volume of the solid formed by revolving teh area bout the x-axis
    h=____?
    DISC or washer method?
    find all the radiuses
    use integration to find the volume...
    x = y^2 + 1

    and
    x= -y + 3 (you may have a typo in your posting)

    intersect at:

    -y+3 = y^2 + 1
    y^2 + y - 2 = 0
    (y+2)(y-1) = 0

    The points of intersection are (5, -2) and (2, 1).

    Draw a picture to decide the method, the area consists of regions in the first quadrant and in the fourth.

    While you could use a combination of disk/washer methods, I would recommend shell:

    x_left = y^2 + 1
    x_right = -y + 3
    Height = x_right - x_left =

    circumference = 2 pi distance = 2 pi y as y ranges from -2 to 1.

    So Volume = Integral (2pi y Height) dy with interval of y values -2 to 1.

    Good luck!!
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