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Integratung a hemisphere

  1. Jul 26, 2014 #1

    bobie

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    Gold Member

    Integrating a hemisphere

    1. The problem statement, all variables and given/known data
    I am self-teaching calculus.
    I'd like to integrate a hemisphere G (http://en.wikipedia.org/wiki/Spherical_cap), where the points of each circle have a given property (k=100x/(√20x)3
    the radius of G r = 10, A = 628.3, h = x
    the top point is A (x=0), a = √20x-x2, and the line AP joining a to a point P is √x2+20x-x2 = √20 x

    I learned to find an approximation by discrete summation, finding the value of y for every slice of G of height 1, (whose area is 20 pi = 62.8) (http://www.wolframalpha.com/input/?i=(sum+[+100x/sqrt(20x)^3,{x+,1,10}])+*20pi) y =352.7

    Now, I'd like to find the exact solution, integrating the product of y by the area of a single circle
    h , I suppose x must be = h as dx must be infinitesimal, is that right?
    http://www.wolframalpha.com/input/?i=integrate+y+=+100+*x/sqrt(20*x)^3+*20pi+x+from+1+to+10) y= 304
    There is a 16% difference, is it too much or everything is OK?

    Thanks
     
    Last edited: Jul 26, 2014
  2. jcsd
  3. Jul 26, 2014 #2
    Last edited by a moderator: Sep 25, 2014
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