fa12_prelim1 - Math 1910 Prelim 1 7:30 PM to 9:00 PM You...

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Math 1910, Prelim 1September 27, 2012, 7:30 PM to 9:00 PMYou are NOT allowed calculators, the text or any other book or notes. SHOW ALL WORK!Writing clearly and legibly will improve your chances of receiving the maximum credit thatyour solution deserves. Please label the questions in your answer booklet clearly. There are6 questions.Write your name and section numberon each booklet you use. You may leave when you havefinished, but if you have not handed in your exam booklet and left the room by 8:45pm, pleaseremain in your seat so as not to disturb others who are still working.1. (20 pts) Evaluate the following integrals:(a)Zcosx+x(2 sinx+x2)2dx(b)Zxsin(x2)dx(c)Z(x+ 1)(x+ 2)100dx(d)Z50|3-x|dx2. (20 pts) A lens is constructed as in the Figure below.This is obtained by rotatingthe region belowy=a, betweenx= 0 andx=band outside the circle of radiusrcentered at the origin, about they-axis.(It helps to draw your own diagram, withall the relevant parts labeled.) Find its volume in terms of the constants

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