MAT1322Solution to Final ExaminationFall 2012SOLUTION TO FINAL EXAMMAT 1322D, Fall 2012Total = 53 marks1.(4 marks) Determine whether each of the following improper integrals is convergent ordivergent. If it is convergent, find its value; if it is divergent, use appropriate method to justifyyour conclusion:(a)01(1)(3)dxxx∞++∫..(b)dx∫.1
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13.(4 marks) Find the length of the arcy=211ln24xx-, 1≤x≤2.
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2.(4 marks) Find the volume of a solid whose base is the region on thex-yplane bounded by thex-axis and the graph of the functiony= 2(1-x2). The cross sections of the solid perpendicular tothex-axis are semicircles with diameter on thex-yplane. Find the volume of this solid.
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