Evaluating the following...

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Math 19B, Summer 2014 MIDTERM EXAM KEY UCSC, Tromba & B¨ auerle 8/15/14 1. Evaluating the following integrals. 1 integraldisplay x 8 dx = bracketleftbigg x 9 bracketrightbigg 1 9 0 9 9 = 1 9
2. Let R be the region between the x -axis and the graph of the function given by y = cos x where 0 x π 2 . Here is a picture of the region (a) The area of the region R is given by integrating cos x over [0 , π 2 ].
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(c) Rotating the region about the axis y = - 1, we get washers with outer radius (1 + cos x

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