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Double (Iterated) Integration. Where am I going wrong?

  1. Jun 30, 2010 #1
    1. The problem statement, all variables and given/known data

    Let D be the region in the x,y-plane enclosed by the curves x = (y^2) - 9 and x = 2y - 6. Find the volume of the solid with base D that lies under the surface z = 1y^2.

    2. Relevant equations

    Fubini's Theorem and Fundamental Theorem of Calculus

    3. The attempt at a solution

    Hello everyone,

    I need some help with a simple iterated integration. I just can't seem to figure out where I am going wrong. According to an online homework site, my answer is not correct.

    I am getting a crazy answer of -179975.2.

    Below is the image of my work. Any help would be GREATLY appreciated, as this assignment is due soon.

    I apologies for the large image for those with small screens.

    [PLAIN]http://img139.imageshack.us/img139/1324/68070772.jpg [Broken]
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jun 30, 2010 #2


    Staff: Mentor

    Your region D is drawn incorrectly. The line intersects the curve at (-8, -1) and (0, 3). You have intersection points of (0, 3), which is mislabeled, and (16, 5). Your point at (0, 3) is below the x-axis, so should be labeled (0, -3).
  4. Jun 30, 2010 #3
    Thank you. The only thing I had to change was the limit of 16 to -9 to 3 to -1 and got the answer correct with the same approach as above. You are correct about the fact that I drew the D region incorrectly... stupid mistake on my part.
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