Example 8.2.1

$f\left(x\,y\,z\right)\=x y z$ 

$R$ is the region in Example 8.1.1

Example 8.2.2

$f\left(x\,y\,z\right)\=x y z$ 

$R$ is the region in Example 8.1.2

Example 8.2.3

$f\left(r\,\mathrm{\θ}\,z\right)\=z r^2\sin \left(\mathrm{\θ}\/6\right)$ 

$R$ is the region in Example 8.1.3

Example 8.2.4

$f\left(r\,\mathrm{\θ}\,z\right)\=r z^2\cos \left(\mathrm{\θ}\/3\right)$ 

$R$ is the region in Example 8.1.5

Example 8.2.5

$f\left(x\,y\,z\right)\=5 x^2\+3 y^2\+z^2$ 

$R$ is the region in Example 8.1.8

Example 8.2.6

$f\left(\mathrm{\ρ}\,\mathrm{\φ}\,\mathrm{\θ}\right)\={\mathrm{\ρ}}^2$ 

$R$ is the region in Example 8.1.14

Example 8.2.7

$f\left(r\,\mathrm{\θ}\,z\right)\=\left(r^2\+z\right) \sin \left(\mathrm{\θ}\/4\right)$ 

$R$ is the region in Example 8.1.15

Example 8.2.8

$f\left(r\,\mathrm{\θ}\,z\right)\={\left(z\/r\right)}^2$ 

$R$ is the region in Example 8.1.18

Example 8.2.9

$f\left(r\,\mathrm{\θ}\,z\right)\=z\/r$ 

$R$ is the region in Example 8.1.20

Example 8.2.10

$f\left(\mathrm{\ρ}\,\mathrm{\φ}\,\mathrm{\θ}\right)\=\sqrt{\mathrm{\ρ}}$ 

$R$ is the region in Example 8.1.21

Example 8.2.11

$f\left(r \,\mathrm{\θ}\,z\right)\=r z \cos \left(\mathrm{\θ}\/3\right)$ 

$R$ is the region in Example 8.1.22

Example 8.2.12

$f\left(\mathrm{\ρ}\,\mathrm{\φ}\,\mathrm{\θ}\right)\={\mathrm{\ρ}}^{3\/2}$ 

$R$ is the region in Example 8.1.26

Example 8.2.13

$f\left(x\,y\,z\right)\=2 x^2\+3 y^2\+4 z^2$ 

$R$ is the region in Example 8.1.27

Example 8.2.14

$f\left(r\,\mathrm{\θ}\,z\right)\=z^{2}r \sin \left(\mathrm{\θ}\/3\right)$ 

$R$ is the region in Example 8.1.28

Example 8.2.15

$f\left(x\,y\,z\right)\=x y^2{z}^3$ 

$R$ is the region in Example 8.1.29