- #1

bobie

Gold Member

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**Integrating a hemisphere**

## Homework Statement

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-x

^{2}, and the line AP joining a to a point P is √x

^{2}+20x-x

^{2}= √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

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