Sections 15.8, 15.9
Homework
MAT329
Andy Long

#16, p. 1055

RevolutionPlot3D[r,{r,0,2},{t,0,2π}]

RegionPlot3D[0<z<Sqrt[x^2+y^2]&&x^2+y^2<4,{x,-2,2},{y,-2,2},{z,-2,2},PlotPoints->35,PlotRange->All]

#30, p. 1055

RegionPlot3D[0<z<9-(x^2+y^2)&&x^2+y^2<9,{x,-3,3},{y,0,3},{z,0,9},PlotPoints->35,PlotRange->All]

Integrate[r^2,{t,0,Pi},{r,0,3},{z,0,9-r^2}]

#37, p. 1062

RegionPlot3D[x^2+y^2<z<2y,{x,-1,1},{y,0,2},{z,0,4},PlotPoints->35,PlotRange->All]

Integrate[r z,{t,0,Pi},{r,0,2Sin[t]},{z,r^2,2r Sin[t]}]

#38, p. 1062

SphericalPlot3D[Sin[phi],{phi,0,Pi},{theta,0,2Pi}]

Integrate[Sin[phi]rho^2,{t,0,2Pi},{phi,0,Pi},{rho,0,Sin[phi]}]
Integrate[1,{t,0,2Pi}]*
Integrate[Sin[phi]Integrate[rho^2,{rho,0,Sin[phi]}],{phi,0,Pi}]