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...Lecture november surface integrals the integral of f x y z over a in r is ds u v dudv where parametric equation when graph one has fx fy dxdy example cylinder cos sin and it obtained using cylindrical coordinates this case we have can use these facts to compute any cone zcos zsin needs sphere spherical sincos fact that implies general be described by zds part lies between as dzd so given becomes d consider lamina occupies paraboloid below plane if its density then mass assume constant for simplicity since switching polar nd rdrd dud...