# 7 . The solid E is the tetrahedron bounded by the planes x = 0 , y = 0 , z = 0 ,
# The solid E is the tetrahedron bounded by the planes xyz and xyz with density rho xyzy Find a its mass, b center of mass, c moment of inertia IZ # Evaluate the integral by changing to cylindrical coordinates first intintsqrtyintsqrtxy xzdzdxdy # Use cylindrical coordinates to find a the mass and b the center of mass of the solid E bounded by the paraboloid zxy and the plane z if E has constant density rho # Use spherical coordinates to evaluate ExydV where E is the solid in the first octant xyz between the spheres xyz and xyz # Evaluate the integral by changing to spherical coordinates first intsqrtintsqrtyintsqrtxysqrtxy xydzdxdy #a Use cylindrical coordinates to write down inequalities describing the solid inside the sphere xyz above the plane zsqrtb Use cylindrical coordinates to only set up an integral or integrals for the volume of the solid. c Use spherical coordinates to write down inequalities describing the same solid. d Use spherical coordinates to only set up an integral or integrals for the volume of the solid. e Using either cylindrical or spherical coordinates, find the volume evaluate an integral
