Solutions to Exam 3 (Purple Version)Ma123 F05

Calculus (With Analytic Geometry)(8th edition)

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Unformatted text preview: joLqucs - gamut a: .. mum/e l. (18 pts.) Consider the two curves shown below: HHIH Fifilil EHHET FUHC a. At what x values do the two curves intersect? 1 21¢ ( 7c ~37 " o b. Write a single integral (don’t evaluate it) for the (shaded) ween the two curves. 2. (13 pts.) Determine the following: d x . a _l t(s1nt) dt = (53.x) 3. (9 pts.) The region below the curve f(x)=x3 +3x2, ISxSZ and above the x—axis, for IS x S 2, is displayed below: HFIIH FiFIIII EHFIIIT FUHE Which of the following is approximating the area under the curve and above the x—axis between 1 . - oose one)? ; iii. 21 - n "it3 i2 iv. ——+3— n) t] Fur rp cleansed“? ("c Jakl. 4‘14 K6771»? mg (he! flaky/3?; Q}, [444' M’Vaiéb 4‘0 0547.; m 50% 4. (46 pts.) Compute each of the following integrals: a.IxJ'-;3dx 5 S “Xi/1‘" Ax: 9/2 V 'L 'X -23‘.+c 37;) (1/1,) H bjx/t—ZTS (Ast45 ‘ H“ ,L A“ JcAJr continued next page 1 ("7:1 Au“- r7.xe *ééu: xéuc $3 '20 ~47: ’- 4x 0 7. *~ 0-“) flclu r. 25" 7(2 2. 2. 5. (19 ts.) The re ion between the curve a. P g :- 2 5‘ _- 7c y = 2" 25—x2 a. x1 t 25 t '7 /+ and the x—axis in the first quadrant is shown below. Note that (5,0) and (0,10) are points on the curve. x : r7; 5 ‘_ 7«/$ Fiv ' sz F3 FH FEv FEv F? S! Took zoom Trace Hear-1H: Hath [Ir-aw Pen =-2 ll ll /f°) HHIH Fifilil EHFICT FUHC a. Write, but don’t evaluate, an integral for the volume of the object obtained when revolving this (shaded) region about the y-axis. 43W 07" (J 15» MW >217 [V (Y D 7C:¢7 K; dzf~o"‘/+ b. Write, but don’t evaluate, an integral for the volume of the object obtained when revolving this (shaded) region about the x—axis. ’7 2 ‘2_ m; ( 5W(zfz;::>147‘ a Hint: The answers to parts a. and b. are different. ...
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