use cylindrical coordinates to evaluate the triple integral

use cylindrical coordinates to evaluate the triple integral sqrt(x^(2)+y^(2)) where e is the solid bounded by the circuluar paraboloid z=16-9(x^(2)+y^(2)) and the xy-plane

Solution

Cylindriacal coordinates x=rcosT y=rsinT z=z At z=0 Region is x^2+y^2= 16/9 , ie a circle with radius R= 4/3 F(x,y) =sqrt(x^2+y^2) = r z= 16-9r^2 dV= rdrdT dz INT_V F(x,y) dV = INT INT INT dz r^2 dr dT 0
use cylindrical coordinates to evaluate the triple integral sqrt(x^(2)+y^(2)) where e is the solid bounded by the circuluar paraboloid z=16-9(x^(2)+y^(2)) and t

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