## rsst123 one year ago ** Will medal ** Calc 3 Can someone show me how you would covert the limits of integration?

2. ganeshie8

what do you know about the surfaces $$z=\sqrt{x^2+y^2}$$ $$z=\sqrt{8-x^2-y^2}$$ ?

one is a cone and the other is a sphere correct?

4. ganeshie8

Yes, something like this ? |dw:1436972486503:dw|

yes

6. ganeshie8

good, setup the bounds for $$\theta, \phi, \rho$$

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

8. 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.

wow that way makes to much sense so ϕ would be 0 to pi/4 ?

11. Empty

Yeah in the first coordinate system yep. =) What's your second question asking?

how would i determine the radius p?

13. 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

ok thanks!

15. 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 $$1$$.