exam%201%20green - Math 152 — Exam 1(Spring 2007 Sections...

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Unformatted text preview: Math 152 — Exam 1 (Spring 2007) Sections 5.1—5.4, 5.6, 7.1—2 Name K €51 ”—— éfeezl Score /100 Show all work t receive full credit. Each problem is worth 6 points unless noted otherwise. 1. Determine the area bounded by the curve y: x: + 2x2 —3x and the x-axis. ¥3+<>9><Q” =3 A Wotan 3x)0(4¢+j0 (x 34'ch (3100626 y(x-l)(x4—3):Ci x9 ,oaiEéE 0 yfi'ofli—B ' "Ejkdgj’3§)]:f(:¥ 3 ';'>]/ ’ ,9 3 a , _ (—339 2(-3)3 313$ fl. , “94-3,! W‘ ’ (9 Jr 3 5L 2“ ( '5 9 . A": 73/ // //s3 2. Consider the curve y = ~27 for l S x _<. 3. (8 points) "lib-3 x a. Calculate the area under the curve on the given interval. 0? 2: 'fi" ,— A $553M” A 3 I '_ l 3 i :7}. :1 ’L 5/3 ’ 3/] A s M a , 3 ’14 ,I b. Determmecso that the line x=c bisects the area of part a. if) jigorw % = 'z% *0? ’7? 4/ ,9. ,. z , 75f] 3 Z E 3 , E g: :3 ._— 2?. z/ I o? I a 3 ‘z- : ’ C”, :2 ~ /o? M 3. Describe in words the difference between total distance and displacement. 02,5?)me méxsafés Mg flak/Me 29.2.wa6 Slap/73 POI/12L QVwQ 7446 Ambit/i? IDOLVLJL‘ 0&5 WM] IS M6 6am 015 +148, Masai/Lute Mates 04 afl We $er ”W455 1B 4. Use disks/washers to determine the volume when the region bounded between y= x2 and y: 5x is rotated :bjz:uttge;—axis. V“: 0377[(5¥)Q (xzyjflk 55555515 )LSOIS {’ iii-(325:5; w [:51]: 5% .. ?[/::3~ 59-03 ,gjg \// 3 77/ 5. The base of a solid is the region bounded by the circle x2 + y2 = 9. Suppose that cross sections perpendicular to the x—axis are squares. Find the volume of the solid. .3 3 :32?me $2155 (9530594 7:35,? ‘HZW: 2133)]: v :5[m- 5H5? 2:3): 25?; 6. Use shells to determine the volume when the region bounded by y = J; , x = 3 , and y 2:: 0 is rotated about thelinex=3. \/: 03W (3 xNiOW i a 7. Use shells to determine the volume when the region bounded between y= x2 and y: 5. x is rotated about :52” M??? w: 2:: :jfiosf/MQ flak :0950/55'169)?’ WM? W'J v a 9%: 2B 8. Determine the length of the curve determined by x= 7cost + 3 and y: 7sint— 2 on [0,71, 015: (4752/1105?!(7m-,péfrfl 95* L“ jfi/a 2 1/9521?” *4/7da52ffiéf , 11/6; ; 7f“??? 0&4 = 7:: 1 9/5‘74f L‘? 9. Determine the surface area for the figure formed by rotating y— — 3%— on [0,1] about the. :-r axis. ds:.I/+(3/¥;)39¢" =077r3 ’ 3/] A/fJ/defi 5:: ‘7 , 01 /4?13fl egglfa’V/a 5km! %Wfl , gas/:12 (Ar/47¢" I 0L“: G’s/$431 5A : /[093£I 3/2) ; 67/ 476/2 I) 10. The density 6 (x ) of a wire at the point x centimeters is given by 6 (x) 2x grams per centimeter. Find the center of mass of the piece of w1re between x: 0 and x: 5 centimeters y; SS’JC'QXc/M, ;°33—¥3jj : if: (W K ”/7”: 59’ mm if i") : 9:" r0717 ”>2“: 439=3é=3§w 11. Find the) center of mass of the region bounded by y: 9— x2 and the x- axis. I 7:0 ——, (31¢ (axis/)1: -— c2 @0156 671011213417) 3 (9 3“ 333 (94311333) ’7) 5 3 a 2 ; M : $2261: 3+ é: '[t/I‘B-M'WC?) J3(9' M23444 3(0 -1) 35—3" W /’ é» 12. Let R be the region in the first quadrant bounded by y = sin x , y = cosx , and the y-axis. (8 points) a. Graph the region R and label the point(s) of intersection. b. SET UP an integral to evaluate the area of R. n/H _ A 50) (ng- 5m X3006 c. SET UP an integral to evaluate the volume, using disks/washers, when R is rotated about the x— aXIS. 4/4 9 / V 7 j 4} 055 94 9a A X) M or (1. SET UP an integral to evaluate the volume, using shells, when R is rotated about the line x = :1: . v; 51m; «mm/1M cosx , 13. Integrate Imdx £22555; pa;f 75:41,; (A: 50’) K ,1 , 2 4B 14. Integrate J2x2+5x+6dx. flip 5X46 x+2 1477’)”, 0’? +/ /f wglmjgs n+6 :W XW’Jfl (37¢ “75! 2 , 3425 @4744 +1/fln/141LQ/M/ 9% to? /7/7’ 15 Integrate I3x1nxdx. BMW ” 51/“va a. Mafia/4 : {7:7— fl: if“ 0&0;4é0éfl “3/37: V 453%”) .. 2 7: “571%? >é’ 3J7 <31? 3252 7M“ 7/“ 7‘4 16. Integrate 1x5 x3 +5 Sclx 33L 5% Oéy, 3 .2 3 ”3/7— (11% V5§ZX+5)/ o? 3 3 3 ’51: 2 2 :: , 6 — 4’ flick 00(23):?» (WW/mm 9 7i (9w ) Lax +5) CKL‘IS "2 3 3 3’3 W532; 312(%3#5)&0a11%j3{[[34/53092 5 6%]; (511/ ' ET 3“ 26¢“ l/L/ X3196 ”ESL/1% 2. 3 3 Sig/4’ £“5/3J/d 050(39me ,ttaawka / 6275M” ? 5 5 ’5 ,3 ’b/ 3 3 $/£L 1/ 3 A2 $51443;st 5B ~71 [1+5)/A75'(1#5) +4 ...
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