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MAT1322D Solution to Final Examination Fall 2016 1 Solution to Final Examination MAT1322D, Fall 2016 BFBCCBCD Part I. Multiple-choice Questions (3 u8 = 24 marks) 1. Let Rbe the region under the graph of y= x3+ xand above the x-axis in interval [0, 1]. Bis obtained by revolving Rabout the y-axis. Then the volume of Solid Bis (A) 158S; (B) 1615S; (C) 54S; (D) 163S; (E) 815S; (F) Answer. (B) Use the cylindrical shell method, the area is A= 113530011162()25315xx xx dxxxSSSªº±±«»¬¼³. 156S. 2.Suppose a surface of the shape of the upper half of a disk with radius 2 meters is submerged into water (with density Ukg/m3) so that the top of the half disk is 1 meters under the water. (See the figure below). Let Dbe the depth of a horizontal stripe of the surface. Let gbe the acceleration of gravity. Then the force acting on this surface is calculate by the definite integral 222222. .
MAT1322D Solution to Final Examination Fall 2016 2 23. Consider improper integral 02dxxx²³. Which one of the following argument is true? 1dxx³diverges, 111111111111