rsst123
  • rsst123
** Will medal ** Calc 3 Can someone show me how you would covert the limits of integration?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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rsst123
  • rsst123
ganeshie8
  • ganeshie8
what do you know about the surfaces \(z=\sqrt{x^2+y^2}\) \(z=\sqrt{8-x^2-y^2}\) ?
rsst123
  • rsst123
one is a cone and the other is a sphere correct?

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ganeshie8
  • ganeshie8
Yes, something like this ? |dw:1436972486503:dw|
rsst123
  • rsst123
yes
ganeshie8
  • ganeshie8
good, setup the bounds for \(\theta, \phi, \rho\)
rsst123
  • rsst123
i understand that θ is 2pi, but i cant figure out how to get ϕ and ρ. I know p is the radius and I think ϕ is the angle between the +z axis but i dont see it
Empty
  • Empty
There are multiple ways to describe the angle \(\phi\). Just imagine the earth as being a sphere of constant radius. You can go around the equator from \(0\) to \(2 \pi\) which corresponds to our \(\theta\) value like you understand but we have two very common ways to talk about the azimuthal angle \(\phi\) which make sense. We can start \(\phi\) from the north pole and call that \(\phi = 0\) and rotate down to the equator \(\phi = \frac{\pi}{2}\) and then to the south pole \(\phi = \pi\) The other way that's commonly done is they'll start with the equator \(\phi = 0\) and say going up to the north pole is \(\phi = \frac{\pi}{2}\) and then say going down to the south pole is \(\phi = - \frac{\pi}{2}\) No method is better than the other, just whichever is most convenient to your problem solving. Generally mathematicians choose the first one and physicists choose the second, but it doesn't matter.
rsst123
  • rsst123
wow that way makes to much sense so ϕ would be 0 to pi/4 ?
rsst123
  • rsst123
and what about p?
Empty
  • Empty
Yeah in the first coordinate system yep. =) What's your second question asking?
rsst123
  • rsst123
how would i determine the radius p?
Empty
  • Empty
Ahhh ok sorry I didn't actually read your question I just saw that you were confused about \(\phi\) and thought I'd help with that give me a sec haha
rsst123
  • rsst123
ok thanks!
Empty
  • Empty
You can determine \(\rho\) from the awesome picture @ganeshie8 made, give it your best guess and try to give a reason for why you think that. If not, tell me what the integral would be if we replaced \(x^2+y^2+z^2\) in the integral with a \(1\).
rsst123
  • rsst123
sorry for the late response I had to take my calc final but the information you gave helped me answer the question on my final. Thanks guys!

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