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Unformatted text preview: i. ji/elﬁe'mf [ MAT 1322A Assignment 2 (Due Wed. Jan. 28th at 8:30) Student Number: 1. Find the volume of the solid obtained when the region bounded by the curves 3; = ﬂ and y = a: is
rotated around the line Answer: Volume = [email protected]_ ‘ l 37 G E E Work: ﬂ» (raff—JZUZIM‘ are: 0.142.494er 0 lVWlff PM“)! (in = l+x
wit; ”AID l‘euf ___ ‘fﬁ +£x mo. I1? /4== ”(qu— ml): ’7 ((7+J3)1 [H7093
: Tr (2J3; _. )t—DLJ) 530% madam {r U: [34/de
1
= ”[615 ~2z 211)a/x = rr (3,32 gal—125 IQ) 2‘ 1T.
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2. Find the volume of the solid whoae base is the region bounded by y z e", y = 1, I = 2 and 5': = 3
where cross— sections perpendicular to the :c—axis are semi ircles.
Answer: Volume = ’.‘_’ (”l 5 8. cl \ 5 Work:
('raxf—J‘c'cﬁonu‘ 4/5 .Q'mmlrc/a‘ ‘3 . of ranging r: :51 (Cxl)
s~ w w Aeeeu (a e
3
A %u;/L£M (J sz’4{TIC/K 3. Find the length of the curve =ex —e ’2 between 1: = D an: :r: = 1.
Answer: Arclength = Q _ ._I.. 1+
e ‘4 Work:
L: fdmgdu '1”!
If" (m) : f{€+;e )dx
6'
:[ “(w—7,79% 2 gnu—w;
/
‘" i — l
’ a e _ .I _ 2
: an I .1? — qe [1
[9 +7 +77 ,7 7/7 4. A tank in the form of a hemispherical bowl of radius 4 m is full of water. Find the work required to pump all of the water to a. oint 2 In bove the tank.
p
Answer: Work: M‘ "l! 5018' X109 3 +51ch or lam; 7 S‘llcb al— lNaixf L
wlll‘ﬁ +£th Ala
96} a. oLlS‘IA mi Maﬁa A” «Jan A (770" 2 71
5f” r1 '" ?la» la:
(And \fét vcluvw. a? tale. 4774.
;g U: AAL “wink; '1T (ELhalrﬁla 7%.: Marc)“ rims/Cf }r M: pl/z /0<3€.‘/7T((Fl7 11),“.
M Ma 9‘0 19: Int/24’ a elm/977cc: cf 64 mefrca S“ 1% .JIrA lr "WW w: Myd= 90%;; (3442)/67U4L
W 777,4 7‘: w: [Veer:71?! was and  WM “we“ 177+ M’ML
20180077 (51W LL” 71p}; )7; GWCH$33)=HC73%3%1TT ...
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 Winter '10
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