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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 => Xssxqux =0 X (x—IHxQ) = 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’XJXQ+°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! [elmxZ] = 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 maxis. (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 yaxis m 41“ mm m z 1 ’X :AXX '1
27:41 =) ’XZOOTZ ...
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This homework help was uploaded on 04/17/2008 for the course MATH 10360 taught by Professor Edgar during the Spring '08 term at Notre Dame.
 Spring '08
 Edgar
 Calculus

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