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

  1. #1
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    Double (Iterated) Integration. Where am I going wrong?

    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 question and I have attached an image of my work. Any help would be GREATLY appreciated, as this assignment is due soon.

    Question:
    (1 pt) Let D be the region in the x,y-plane enclosed by the curves and . Find the volume of the solid with base D that lies under the surface .

    Answer (my work, please click on the image link):

    Double (Iterated) Integration. Where am I going wrong?-68070772.jpg
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  2. #2
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    The first thing I can see that is wrong is that your dx and dy are around the wrong way.

    That would mean that when you integrate with respect to y first, it should be noted that the y values are bounded by y = \pm \sqrt{x + 9} and y = \frac{1}{2}x + 3.
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  3. #3
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    Your graph is also wrong. What you have marked as (0, 3) should be (0, -3), because it below the y-axis, and is NOT a point of intersection of the two graphs.

    If x= y^2- 9 and x= 2y- 6 then x= y^2- 9= 2y- 6 so that y^2- 2y- 3= (y+ 1)(y- 3)= 0. The two graphs intersect where y= -1 and y= 3. When y= -1, x= -8 and when y= 3, x= 0.

    The two graphs intersect at (-8, -1) and at (3, 0).
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  4. #4
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    Thank you. My D region was incorrect. I only had to change my integration limit from 16 to-9 to 3 to -1 an got the answer correct using the same approach I used.
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