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Rectangle volume using cross sections

  1. May 23, 2012 #1
    1. The problem statement, all variables and given/known data
    Cross sections are perpendicular to the x axis and rectangle has the h=1/2b. The region is bounded by the area y=x^2, x axis and the line x=3


    2. Relevant equations



    3. The attempt at a solution
    A=BH
    A=B(1/2B)
    A=3/2B
    V=3/2(x^2-3)

    just wondering if this is correct and how would i find where i integrate it to?
     
  2. jcsd
  3. May 23, 2012 #2
    Calculus aside, the last statement is wrong.


    And do your problems lie in finding the limits of integration?
     
  4. May 23, 2012 #3
    Ok so we will be integrating between x=0 and x=3. This is due to the region being bound by x=3 and y=x^2 (where y=0 @ x=0).


    Therefore, V = (0∫3)* (x^2)(0.5(x^2)) dx

    height (1/2b)-----------------^
    base------------------^
    -----------------^upper and lower limit of integration

    A plain square would be calculated like this:


    Therefore, V = (0∫3)* (x^2)(x^2) dx

    *This is the format (lower limit∫upper limit)

    Hope this helps, if you have a question let me know.
     
    Last edited: May 23, 2012
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