Practice Midterm Math 19B Spring 16.pdf - Practice Midterm...

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Practice Midterm Math 19B (Calculus 2)UCSC, Robert Boltje, Spring 2016Time:90 minutesNo calculators, cellphones, notes or other tools allowed.1.Compute the following definite integrals:(a)R1-3(x3)dx,(b)Rπ-πcos(θ),(c)R21ettdt.2.Find the area of the region bounded by the curvesy=ex,y= 2 andy= 1-x.3.Find the derivative of the functionA(x) =Rx-1et2dt.4.Compute the volume of a ball with radiusR(a) using Cavalieri’s principle,(b) using the shell method.5.Assume a rope of length 10mhas thickness 10mmat the one end andthickness 20mmat the other end and that the thickness varies gradually:

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