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Find the volume of the solid

  1. May 22, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the volume of the solid generated by rotating the region enclosed by y=sqrt(x+1), y=2x/3, and the x-axis about the x-axis



    2. Relevant equations
    Disk/washer method, shell method



    3. The attempt at a solution
    This question seemed easy enough, as I found the points of intersection for the 2 functions (these points being -1 and 3), then plugged each of these functions into the disk/washer method equation and tried to solve over [3,-1]. This did not get me very far, for I ended up with an answer higher than the 4pi I should have gained. This is the way I set up the equation:
    V=pi[tex]\int(x+1-(4x^2/9))dx[/tex] (I already applied the squares to the functions inside the integral). I am wondering if I made a mistake setting this question up, or if I made a mistake with the closed interval I used. If anyone can point me in the right direction for this question it would be greatly appreciated, thanks in advance.
     
  2. jcsd
  3. May 22, 2009 #2
    Hi. You need to plot it carefully and look at it: the lower boundary of the region is the function y=2/3x in one part of the region, but is the x-axis in the second part of the region. So . . . break it up into two integrals.
     
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