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MA113_2010SPRING_EXAM1__[0] - MA113(Calculus II Midterm...

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MA113 (Calculus II) - Midterm Examination # 1 March 2, 2010 4:05pm-5:55pm Write your name on your exam sheet AND booklet(s), and please show all work. The exam is out of 100 points. 1. [30 pts.] Set up, but do not solve integrals that calculate the desired quantity (you don’t need to start from first principles and do rigorous derivations (i.e., Riemann sums, etc.), but pictures and word explanations may be helpful in determining partial credit, and should definitely accompany your solutions). (a) [3 pts.] the arclength of the curve r = 1 θ 2 for θ π/ 2 (b) [4 pts.] the volume of the solid obtained by revolving the portion of the graph of y = x 4 + x + 1 above - 1 x 1 about the line x = - 1 (c) [4 pts.] the volume of the solid obtained by revolving the portion of the graph of x = 1 y above 2 x 3 about the x -axis (d) [4 pts.] the area of the intersection between the region bounded by r = 2 cos 3 θ and the region bounded by r = 1 (e) [5 pts.] the coordinates of the centroid of the triangle with vertices ( - 2 , 0), (1 , 3), and (1 , 4) (f) [5 pts.] the surface area swept out when the upper half (
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