Solving for Volume in a Complex Figure: Ostrogradsky and Spherical Coordinates

[DianaSagita]

Volume Integral! Help!

I need help with this:

Find volume of figure bounded with surface (x^2+y^2+z^2+1)^2=8*(x^2+y^2)

I tried Ostrogradsky, and spherical coordinate system with it, but I can't find boundaries...

PLEASE! HELP ME!

 

[quantumdude]

Please show us what you tried, then we'll help you. That's the policy here.

 

[tiny-tim]

Welcome to PF!

I need help with this:

Find volume of figure bounded with surface (x^2+y^2+z^2+1)^2=8*(x^2+y^2)

I tried Ostrogradsky, and spherical coordinate system with it, but I can't find boundaries...

PLEASE! HELP ME!

Hi DianaSagita ! Welcome to PF!

(what's Ostrogradsky? )

(oh, have a squared: ²)

Hint: it's obviously cylindrically symmetric, so write x² + y² = r², to give:

(r² + z² + 1)² - 8r² = 0.

 

[DianaSagita]

Thanks a lot. I did it! :)