I need to find the volume of the object:
$z = 3 + \cos x + \cos y$, over $x = 0$, $x = \pi$, $y = 0$, $y = \pi$
The only formula I know if integrating $f^2(x)$ and multiplying by $\pi$. How does it work for 2 variables? I know multivariable integrals, just not how to implement them here.
I don't think this is a solid of revolution at all. It is a box, with the base a square of side $\pi$ and the height given by $z$. Then the formula for the volume is $$V=\int_0^\pi dx\int_0^\pi dy\ z(x,y)$$ This should be an easy integral, but let me know if you have problems with it.