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w07final

# w07final - Math 42 Calculus Final Exam Name Section...

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1. (9 points) Let R be the region bounded by the curves y = f ( x ) and y = g ( x ) shown in the graph below. - 4 - 2 2 4 x 4 - 2 2 4 y f H x L H - 3, 2 L H 2, - 3 L g L (a) Set up a deﬁnite integral that will give the area of the region R . (b) Set up a deﬁnite integral that will give the volume of the solid generated when the region R is revolved about the line y = 4. (c) If the base of a solid V is the region R , and if all cross-sections of V that are perpendicular to the x -axis are squares, set up a deﬁnite integral that will give the volume of V .
2. (10 points) According to Newton’s Law of Gravity, an object near the earth at a distance of r meters from the center of the earth feels a gravitational force of F = k/r 2 Newtons, where k is a positive constant that depends on the mass of the object.

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w07final - Math 42 Calculus Final Exam Name Section...

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