Find average velocity of a sphere which expands and moves

[haruspex]

Can dtheta and dphi change sides

Do you mean, can they be in either order? Yes. It's the order of the integral signs that defines the order of integration (inside first).

 

[Quarlep]

I am in holiday I am not working in computer so I can't write all steps to you right now.We will do first integral (the one which is inside) that's phi but there wrote dtheta so I asked you this

 

[Quarlep]

Can you tell me what was that please the only thing I ll do is put it on program

 

[haruspex]

Can you tell me what was that please the only thing I ll do is put it on program

Sorry, I don't understand what you are asking.

 

[Quarlep]

The answer :):)

 

[haruspex]

The answer :):)

Do you simply want the answer to the original question, by whatever means, or do you specifically want to see how to do it through an elaborate double integral?

 

[Quarlep]

I want to see answer to the original question

 

[Quarlep]

I am working on symbolab but I found nothing

 

[haruspex]

I want to see answer to the original question

Then use my symmetry method. It gets rid of the trig terms and makes the integral trivial.

 

[Quarlep]

I was banned so I couldn't answer over a 10 days I found 4p(pi)r^2((v'^2)+v^2)

 

[haruspex]

I was banned so I couldn't answer over a 10 days I found 4p(pi)r^2((v'^2)+v^2)

I think it should be exactly half that.
Note that the factor outside the parentheses is just the mass.

 

[Quarlep]

Thank you so much. Problem is solved now.