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+∫. 1111
2.(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.