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...Advancedcalculus final exam june a points let r be the triangular region in rst quadrant bounded by lines y x and usefubini theorem to evaluate z sinxdxdy solution for each consider function sinx f if since lim is continuous on hence integrable dxdy dydx sinxdx cosx b ye now e dx xe xdx continued c t tx comparison test show that log xy s zz usethechangeofvariables da k u v contained cube with side length m ns kf mkx yk all we have diameter of max ofk which implies page compact set content zero has there exist nite collection kj j n cells such sinceahasmeasure thereisacover ofabyopenrectangles...