# S 15-3 - Math 200 Spring 2010 Worksheet#19 Name ﬂ7—...

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Unformatted text preview: Math 200, Spring 2010 Worksheet #19 Name ﬂ7—__ Section 15-3 Triple Integrals 1. Evaluate the triple integral of f (x, y,z)=( x 2 over the box B=[0,2]x[2,4]x[-1,1]. y+z 53TH, ' ‘1‘ 1 x ‘ s I 1 J‘IJQAUL I dxa a; = l _L 1 2 6 I _ 2§°f(y+2)1 I ﬂifwﬁy-Eujx- db,” :j‘fz—ryﬁ): dye”, :1 f_. —2_’..-___.. ‘1 : [I- L + g ‘0 -i 1‘ .4 (y'tiX )1; _‘ ( +1.1 1+a)d2 '-’ [~251an+.}] +QJM\1+.2 x y - 1* 2. Evaluate LZJtyzdzdydx : _ 3&5 't- 1%.? 1" 23m? “lid : —1_gms +lgagaﬂk—é-m 1 21: '3 f 3 2:7 I 2’ l __ a J z 1 __ y-lx ° “it DWI“ y“ oinyd’d" ” Illa ~t1w ‘” o _ ._ \$___L S _ ' ‘ 5 l — “ﬁx _ .12 5 -. L5 -L - 1.5. — _5_ oj( t” )d" a} ‘j-XJX ' *1— 61‘ o i’ it; u 5’ 3-. Evaluate HIVde , where Wis bound by the parabolic cylinders y = x2 and x = y2 and the planes 2 = 0 d = . 'l')’ I 'l r in 175er 93x7.” -. [37ka alqu 1 3:;dk d7“ 7% W ° 7“ o : I ll“)! {ht-r, l J]; 1 J- j[ mar”, ~f Jﬂ}, m ‘l Ire~ x l O x" 2. 7 Ivy 3 x .6 j l . ' \ — 3 .6 7 *3: *6“ 1:2?“ 1‘7 “*2 m: «H g 5 e» was-max y—PQKe G ebLU' IQ“? v __ El 3. 7 I 7 5, J - J‘ 3' ‘ d 3 - P 7 ‘ 8x illx/x'ﬁX‘z‘l‘IX lo " 3' +2! P1 :11"? "'13 4. Integrate f (x, y,z) = 2 over the region lying below the upper hemisphere of radius 3 and above the triangle in the xy-plane bounded by the lines x = l , y = Oand x = y . “l a. I- t _ a 1 Ufle-kelePbET-e 53%;” : 9“)! :7 :jfi‘i‘zi-‘ISQ‘X “7 x‘+)‘+2.~1=9, 230 w a ‘51 “1de a o 2 i=0 4"” l l 000 l. X 2, 2. : ‘l-qc—y :j1-iz__L3 ‘3 I 7 ‘ jg) _2 d?“ In? 2M 67) ‘5‘ ‘ (Eh—trap I'PJleA. ' 0 ° - . ‘ 1 I r ., x II " - -_- I ._-.l. :ﬁ-iz-zév Ul' ltnygﬂofefllquirl) ofyixjogxgl} ofax 32c 012‘ ‘1 6x a ‘ié n. 5. Evaluate de , where Wis bound by the planes y = O, z = 0, x+ y = 2 and the cylinder y:1 + 22 =1 in‘the ﬁrstoctant. N * §(§VI%)\o£yi1lbé 2 5 {1731‘} 6 ﬁg 52...)? +7?“ ‘ 6T5 :2- region 2w: 7j 7 Mr: e. ojof U. 2dxdedy : jf(:7)3da-oly I 2:61;. 6 s y : L l. _ I l h 672 ML“, ;1 *1 we», =§J u~7-2,‘+;)ay 2 ﬁbrirk'ﬁfﬁnd " Jill'i‘i *3?) '-’ if? 6. Use a triple integral to ﬁnd the volume of the solid bounded by the cylinder y = x2 and the _' planes 2:0, 2:4, and y=9 w: {(ﬁsz‘tll-lnég A157“; 0 sass} - 3 cl If 3’ ‘1 r v j 3 _ xi: afdidydx lawlny : Lf-[Fi-dldyt ‘3 3 -3); 3‘ : #23)th 1 3 HfN-‘Hn-‘Q :1er *3 7. Find the average of f(x,y,z) = xysin(7rz) over the cubeO S x, y,z 31. pm 0‘ me) i " ﬁﬁllwm -' +535» 5“" (“3°”) ' 555cm: 5 “ w ' f 1 i H) I 4.71. ‘ fffxy sin (nededez = IX“ 5 ydyfwﬁm LJ‘ 5 0 o 6 a o \ I x) l i}. I i l -L i ’L UOVme : 2 ~- - I _ : _L,_t : 1 1° 1° (“tun-2H0 3 J[ﬁ-tn) 2w 8. Find the mass and center of mass of the solid Wwith density p(x,y,z) = 4 that is bounded by the parabolic cylinder z=l—y2 and theplanes x+z=l, x=0, and 2:0. M L ' a “jtfy[£_ all _ X7 _5 I Iiide _ I is): I I 2 J :0 ~Jj-[d-yfl7)_27n_yrﬂd ‘ ° ° “'17 ‘ I (‘f ‘ 32. n 7 ‘l 5 2H1? “ "" 3f 5 _ . M is I?) ycn 2%:0) ﬁcﬂ:é¥:% LTLfraerw I-S odd} Homework #19 Reread Section 15.3 (Due 03/26) Do Section 15.3 Exercises: 3, 7, 13, 17, 19, 23, 25, 29, 30, 33, 34, 36 Prepare for next class session: Read Section 15.4 ...
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S 15-3 - Math 200 Spring 2010 Worksheet#19 Name ﬂ7—...

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