- #1
robertjford80
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Homework Statement
I'm just interested in knowing where the 4 comes from in front of the integral.
Measuring volume of spheres using triple integrals
- Thread starter robertjford80
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I'm just interested in knowing where the 4 comes from in front of the integral.
- #2
tiny-tim
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hi robertjford80! 
that 4∫0π/2 is really ∫02π …
i suppose the writer thought it looks confusingly like ∫00, though i see nothing wrong with it!
that 4∫0π/2 is really ∫02π …
i suppose the writer thought it looks confusingly like ∫00, though i see nothing wrong with it!
- #3
robertjford80
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Ok, pretty unexpected but I guess it makes sense.
- #4
HallsofIvy
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In other words, they are using the circular symmetry of the figures, integrating from 0 to \pi/2, rather than from 0 to 2\pi, then multiplying by 4.
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Hello,
This is the attachment, the steps to solution are pretty clear. I guess there is a mistake on the highlighted part that prompts this thread.
Ought to be ##3^{n+1} (n+2)-6## and not ##3^n(n+2)-6##. Unless i missed something, on another note, i find the first method (induction) better than second one (method of differences).
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