Midterm-1st Version.pdf - Math 19B Fall 2014 MIDTERM EXAM...

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Math 19B, Fall 2014MIDTERM EXAMUCSC, B¨auerle/Tromba, 11/08/14Notes:Put your answers in the provided boxes. Scientific calculators are allowed, but no programmableand/or graphing calculators. And please put away your cell phones and other electronic devices, turned offor in airplane mode. Put your answers in the provided boxes.Your Name:Your Score:/80 Last Initial:1. (20 points, 5 each) Evaluate the following integrals.(a)1Z0x10dx=(b)Zx2sin(x3)dx=(c)π4Z0sec2(x)etan(x)dx=(d)Z1x(lnx)2dx=2. (20 points, 5 points each) For this problem letRbe the region between thex-axis andthe graph of the function given byy=exwhere 0x1.(a)Set upan integral (butdo NOT evaluate) that gives the volume of the solidgenerated by rotatingRabout thex-axis.(b) Find the volume of the solid generated by rotatingRabout thex-axis.(c)Set upan integral (butdo NOT evaluate) using the shell method that gives thevolume of the solid generated by rotatingRabout they-axis.(d) Find the volume of the solid generated by rotating

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