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Find the moment about the y-axis

  1. Nov 3, 2009 #1
    Given the region defined by y=6(x)^.5-4 and y=6x^2-4 with density p, Find the moment about the y-axis

    I found the upper bound but coulden't find the lower bound.

    and i just want to make sure i set up the equation right

    my=p[tex]\int[/tex] (x)((6(x)^.5-4)-(6x^2-4))dx

    I used the shell method in case i confuse anybody
     
  2. jcsd
  3. Nov 3, 2009 #2

    Mark44

    Staff: Mentor

    Actually, you used thin vertical strips, not shells, which are used when a region is rotated around an axis. By "lower bound" I assume you mean the bottom limit of integration. Set 6sqrt(x) - 4 = 6x2 - 4, and solve for x. You should find two values of x. Those are your limits of integration.

    Other than that, your integral looks fine.
     
  4. Nov 3, 2009 #3
    so if i set those two equation up i will get
    6x^.5(-x^(3/2)+1)
    which will give me 0 and 1 right?
     
  5. Nov 3, 2009 #4

    Mark44

    Staff: Mentor

    You should have an equation.
    6x^.5(-x^(3/2)+1) is not an equation.
     
  6. Nov 3, 2009 #5
    i just set it to 0
    6x^.5(-x^(3/2)+1)=0
    6x^.5=0
    x=0
    -x^(3/2)+1=0
    x=1
     
  7. Nov 3, 2009 #6

    Mark44

    Staff: Mentor

    OK, that's an equation. And yes, the x values at the intersection points are at x = 0 and x = 1. BTW, there are two more values of x, but they are complex.
     
  8. Nov 3, 2009 #7
    do they involve imaginary number?

    + and - i????
     
    Last edited: Nov 3, 2009
  9. Nov 3, 2009 #8

    Mark44

    Staff: Mentor

    Yes, but since you're interested only in real solutions, you can ignore them.

    What I did was solve 6sqrt(x) - 4 = 6x^2 -4 ==> 6sqrt(x) = 6x^2 ==> sqrt(x) = x^2. I squared both sides to get x = x^4 ==> x(x^3 - 1) = 0. The left side can be factored.
    x(x - 1)(x^2 + x + 1) = 0, so x = 0, x = 1, or x^2 + x + 1 = 0. The quadratic has complex solutions.
     
  10. Nov 3, 2009 #9
    YES can't believe i still remember stuff from cal 1 haha thanks so much u r AWESOME!!!!!
     
  11. Nov 3, 2009 #10

    Mark44

    Staff: Mentor

    Thanks much! I appreciate the feedback.
     
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