MAT1322 Solution to Final Examination Fall 2012 1 SOLUTION TO FINAL EXAMMAT 1322D, Fall 2012 Total = 53 marks 1.(4 marks) Determine whether each of the following improper integrals is convergent or divergent. If it is convergent, find its value; if it is divergent, use appropriate method to justify your conclusion: (a) 01(1)(3)dxxx∞++∫. . (b) 23012dxxx+∫. 11112.(4 marks) Find the volume of a solid whose base is the region on the x-yplane bounded by the x-axis and the graph of the function y= 2(1 −x2). The cross sections of the solid perpendicular to the x-axis are semicircles with diameter on the x-yplane. Find the volume of this solid. 3.
(4 marks) Find the length of the arc y= 211ln24xx−, 1 ≤x≤2.
MAT1322 Solution to Final Examination Fall 2012 2 2112= 2111++=+. =