Example 8-2-6 - Maple Help



Chapter 8: Applications of Triple Integration



Section 8.2: Average Value



Example 8.2.6



 Obtain the average value of $f\left(\mathrm{ρ},\mathrm{φ},\mathrm{θ}\right)={\mathrm{ρ}}^{2}$ over $R$, the region that is bounded inside by the surface $\mathrm{ρ}=1+\mathrm{cos}\left(\mathrm{φ}\right)$ and outside by the sphere $\mathrm{ρ}=2$. (The variables $\left(\mathrm{ρ},\mathrm{φ},\mathrm{θ}\right)$ are spherical coordinates.) (See Example 8.1.14.)