APPM 1360 Midterm: appm1360spring2016exam2_sol
Document Summary
Spring 2016: (28 pts, 7 pts each) for each of the following parts, let f (x) = x2 + 2 and g(x) = 4 x2. 2 (2 x)(cid:2)(cid:0)4 x2(cid:1) (cid:0)x2 + 2(cid:1)(cid:3) dx. H(cid:0)7 x2(cid:1)2 (a) washer method: v =z b. Shell method: v =z 4 (b) shell method: v =z b. 2 (y + 3)(cid:16)2p4 y(cid:17) dy +z 3. 2 rp1 + (x )2 dy =z 6 a p1 + (y )2 dx =z 2. 2p1 + 4x2 dx. a (c) s =z b. 2 (d) since f (x) = 2x and g (x) = 2x, the arc length integral is the same for both curves: Locate the centroids of the smaller regions and use additivity of moments to con rm your answer for part (b). Solution: this problem is similar to hw 7. 6 #50. (a) the equation of the line connecting the points (0, 5) and (3, 2) is y = x + 5.
