Calculus II PLTLFall 2014Worksheet 2These problems are to be do ne without the use of a calculator unless otherwisespecified.(Small Groups) Talk about how you have been studying for the first exam. Whattypes of questions do you think will be on the exam? How much practice do you thinkis necessary to do well? Do you have a tried-and-true study method that yo u would liketo share with the group? Do you study alone? In groups? Do you visit the professor’soffice hours? Walk-in help? Review sess ions? What will you do if you need help withsomething?1) (Pairs) Sketch each region on the board without using a graphing calculator and usean integral to compu te the ar ea of the region.(a) The region between the curves y = exand y = e−xand the lines x = 0 and x = 1.(b) The region between y = s in x and y = 1 forπ2≤ x ≤3π2.(c) The region between y2= 2(x − 3) a nd y2= x.2) (Round Robin) Let f(x) = x3and let R be the region between the graph of f andthe x-axis on [0, 2]. (Fun fact: A region such as R i s cal led a cubical spandrel.)(a) Use the shell method to find the volume of the solid o btained by revolving Rabout the y- axis.(b) Check your answer usin g the washer method.3) Find the length o f the curve y =112x3+1xfor 1 ≤ x ≤ 3.4) (Pairs) Find the volume of the solid whose base is the region in the xy-plane boundedby the circle x2+ y2= 9 0 0 and w hose cros s-sections perpendicular to the y axis aresemicircles.5) (Scribe) Let y =Rx313√t dt. Find the value ofdydxat x =
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