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I Should we consider negative axis when finding the volume?

  1. Dec 21, 2016 #1
    Find the volume of the solid obtained by rotating the region
    bounded by the given curves about the specified line. Sketch the
    region, the solid, and a typical disk or washer.
    y2 = x; x = 2y; about the y-axis

    Solution: http://www.slader.com/textbook/9780...-transcendentals-7th-edition/438/exercises/9/

    Now, when I solved the question, I multiplies the entire integral by 2 since the limits I took were from -2 to 2. However, in the answer, they have considered only the values above the x-axis and not below. Why is it so? It doesn't specify in the question that we need to find the area of only that region which lies above the x-axis.
  2. jcsd
  3. Dec 21, 2016 #2


    Staff: Mentor

    This doesn't make any sense. The two curves intersect at (0, 0) and (4, 2). What does your integral look like?
    The region that is being revolved around the y-axis is completely above the x-axis, except the point (0, 0). Did you sketch the region that is being revolved?
  4. Dec 21, 2016 #3
    Okay, I got it. Just one question, when we plot x=y^2, why don't we plot it below the x-axis as well? I know that it will cease to be a function, but we can values for x when we take y and -y, right? (That's what got me confused, I plotted y^2=x as y=x^2 but turned 90 degrees. Which made me draw another line below the x axis as well for some reason-- stupid me!)
  5. Dec 21, 2016 #4


    Staff: Mentor

    You do plot a part of it below the x-axis. But, the region that is being revolved is between this curve and the line x = 2y. That region is completely in the first quadrant.
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