How Do You Calculate the Volume of a Tetrahedron Using Integrals?

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http://mathpost.asu.edu/~shotwell/mat272/hw/pp.pdf
 
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Welcome to PF shg8505. The policy of these forums is that when you post a homework problem, you should also post some work you've already done, or at least an attempt -- no matter how stupid you may think it is or how far off you think you are :smile:

We can always just solve the problem for you but
a) It's your credit you want to earn, we (at least, the ones that would solve the problem) have probably already passed your course
b) We wouldn't know if you would just copy the answer or you would really understand what you did, and when you don't give us an idea about the level you're on it's hard for us to explain it properly.

If I read the problem, I'd say it's just plugging in the given information. So please be more specific.
 
number one is the only one i need help on. i don't even know where to start and i can't reach the prof until after thanksgiving
 
You need to write down an integral that covers the volume of the tetrahedron. Can you make an attempt to do so?
 
Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
The value of H equals ## 10^{3}## in natural units, According to : https://en.wikipedia.org/wiki/Natural_units, ## t \sim 10^{-21} sec = 10^{21} Hz ##, and since ## \text{GeV} \sim 10^{24} \text{Hz } ##, ## GeV \sim 10^{24} \times 10^{-21} = 10^3 ## in natural units. So is this conversion correct? Also in the above formula, can I convert H to that natural units , since it’s a constant, while keeping k in Hz ?
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