Set up the triple integral of an arbitrary continuous function

f$($x$,$ y$,$ z$)$

in cylindrical or spherical coordinates over the solid shown.

$7$

$10$

The x$$y$$z$-$coordinate system is given. A portion of a sphere of radius $10$ centered at the origin is given. The first octant, the concentric sphere of radius $7,$ and the portion below the x$$y$-$plane have been removed.

$$f$($x$,$ y$,$ z$)$ dVE

$=$

$0$

$2$

$10$

f$$

$,$

$,$

$$

d$$ d$$ d$7$