act4_sol - i Wt Solu‘iioms‘ Name . . . . . . . . . . ....

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Unformatted text preview: i Wt Solu‘iioms‘ Name . . . . . . . . . . . . . . . . . . . . . . . . (Math 10360) Group Activity 4 Area and Volume, Disk and Shell Methods 1. For this problem we want to compute the area of the region bounded between the graphs of f(x) = x3 — 3x2 + 2x, g(a:) = 0. (i) Find the intersections of f and g. (ii) Sketch the graphs of f and g and the region between f and 9. (iii) Compute the area of the region obtained from (ii). (iv) Is it true that the area of a region bounded between f and g from :r = a to m = b always equals f — dm? Give an explanation. U), {WWSHJ => Xs-sxqux =0 X (x—IHx-Q) = o 3 X T 0,1,2 (in '3 2 (m) Am“ I _('x—-3)<+2x)dx O 4 1 L 4 : -— + _ .. 4 4 Z 1 (W) NO ) )5 moi iifuc, 2 3 - ENC/Wm, i’X-JXQ+°2X so whun and .- 2. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the y—axis. x y=e, x21, y=1 Dile CZ “lb if — ‘l (N 4 :1: E M T TI [eilmfl -3]: : ll (32+|) Slull Helth -Iolv‘ e V= mt 37(E1~l)o\x I ><'z e 2 21Tl(_ _ xldx ‘x 2 'Le -’ 2 2T! [elmx-Z] = we 2| 2 3. (Solids with knowri cross section) Find the volume of the solid Whose base is bounded by the square centered at the origin with sides length 2 with the indicated cross section perpendicular to the m-axis. (a) Triangle of variable height h = cos x. (b) Rectangle of variable width 10 = x + 1. M < h; cm 2 I I V ' Smedx a Svnx] cl _l = 3W(i)'Slrw(-—n : Slm(1)+slmu) = ZSim (1) (b) “:14” I \ ’2 V «‘ l2rx+no\x = 2 [2‘ +X] m “I 2 .‘ bofitzz 3 - 2lfl+1-_1 +1) : 4 - 2 2 4. Use the shell method to find the volume of the solid generated by revolving the plane region bounded by y=m2J y=4a¢—m2 about the y-axis m 41“ mm m z 1 ’X :AX-X '1 27:41 =) ’XZOOTZ ...
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act4_sol - i Wt Solu‘iioms‘ Name . . . . . . . . . . ....

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