1124worksheet8

1124worksheet8 - Polytechnic Institute of NYU MA 1124/1424...

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Polytechnic Institute of NYU MA 1124/1424 Worksheet 8 Print Name: Signature: ID #: Instructor/Section: Directions: Show all your work for every problem. Problem Possible Points 1 10 2 15 3 15 4 10 5 10 6 10 7 10 8 10 9 10 Total 100 1

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2 (1) Given the region bounded by the curves y = - x , y = x - 6, and y = 0: (a) Sketch the region. (b) Represent the area of the region in terms of x . (c) Represent the area of the region in terms of y . (d) Find the area of the region.
3 (2) Given the region bounded by the curves y = 2 x , x + y = 9, and y = x - 1: (a) Sketch the region. (b) Represent the area of the region in terms of x . (c) Represent the area of the region in terms of y . (d) Find the area of the region.

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4 (3) Sketch the region bounded by the curves and ﬁnd its area. (a) x + y 2 - 4 = 0, x + y = 2. (b) y = cos x , y = sec 2 x , x [ - π/ 4 ,π/ 4]
5 (4) Given the region bounded by the curves y = x 2 and y = x + 2. Find the volume of the solid generated by revolving this region around (a) the x -axis (b) y = - 4

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1124worksheet8 - Polytechnic Institute of NYU MA 1124/1424...

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