# cal2final - MAT1322 Solution to Final Examination Fall 2012...

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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
13.(4 marks) Find the length of the arcy=211ln24xx-, 1x2.
2302xx+111
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.
MAT1322Solution to Final ExaminationFall 20122112=2111++=+=
2
4.(5 marks) A monument of the shape of a truncated circular cone is built with stone of density5000 kg / m3. The radius of the bottom of the monument is 3 meters, the radius of the top is 1meter, and the height of the monument is 20 meters. (Recall that the radius of the cross section atheighthis 3-h/ 10 meters). Find the work (in Joules) needed to lift the stone from the groundlevel to build the monument. (Useg= 9.8 m/sec2)

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