1ab - MA 241 Test 1 Form E Spnng 9 Set 11 ONLY a b and c...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MA 241 Test 1 Form E ) Spnng 9. Set 11 ONLY a b and c below. Insert all numerical values so that if you had a calculator, you could finish the arithmetic. a. Use Simpson’s Rule with n=4 subintervals to approximate 3 x f—dx 1 1 + (sin x)2 b. Find the area of the region R bounded by the line y=x and the parabola 2 y=6—x_ c. Find the volume of the solid generated by revolving the region in part b (previous area problem) about the line y=10. 10. Decompose to partial fractions (this is not asking for integration!) x (x + 3)(x — 2)2 Continue on the next page Form B continued 11. Integrate. x a. ——dx fx+l b. I coshxg + 3) dx 6. f xzedex d. fxln(5x) dx x-2 . ————dx 6 f(x2-4x+l)2 12. Determine if the improper integral converges or diverges. If it converges, evaluate. °° l f 2 dx 0 x + 4 13. Use the appropriate formula, if needed, from the given ones list below from the Tables of Integrals to integrate x e f 2x dx 3—6 . Table of Integrals: du l u+a a. = —ln +C faz —u2 2a u—a du l u—a b. = —ln +C fuz —a2 2a u+a Fab .9 200 _ b flag» l, a u L V . AVI 9U’Xz 1+ x” ' :0 L x+37 x-2)= 0 >002 ' «l0 . v . . C v",' ' 3' .0. M0 l l. (A. 224’ M ‘ ’ ‘ ' ’ AWL“ ML?- , o 2 2 ~ R'dx '.“'_.n -. A ;.‘._,~‘,-4.'_aum:z~ v...” u -' -* ~ Fawn E, p31 - ‘- ; X’Z + x+’$ X-z + 4?; — =A- ~22+-3+3)—*2+z/-+3 -:- 7-.» o— +2 . Pom E, 733 j, I“ I"; L i ' MA 241 Spring 2007 Test 1 solution key 1 1 (a) Integrate a: /$+1dx Solution: This fraction is improper, hence we perform division. ___.__1 as + 1) a: —m—1 — 1 Therefore :1: _ 1 _ 1 x+1— x+1 And we now integrate ll x 1 /x+1d$ _/(1_x+1>dx flair—f 1 d9: x+1 m—ln|m+1|+C H 11(b) Integrate \/_ cos( x + 3) / —\/E da: Solution: Use u—substitution. 1 u=\/§+3, duzmdcc Integrate: cos(\/E + 3) _ cosfi/E + 3) = 2/cos(\/§+3)—}——dx 2% 2 / cos(u)du 2 sin(u) + C 2 sin(\/§ + 3) + 0 Pink version _____ __<_A___T_.,.=A,_1 ._‘_..A‘. -«1- __......_._.4_ ._..._V 11(c) Integrate 1. E? 2 x3 an 6 dx i! Solution: Use u—substitution l u = x3,du = 3x2da: /:I:26$3d117 % f BmZexsda: % / eudu 1 = geu + C = $623 + C 11(d) Integrate / m1n(5:c)d:c Solution: Use integration by parts (LIATE) 1 5 1 i u = ln(5x), du = 5—mdx = de I 2 a: du — a: (1512,12 — —2— f x ln(5m)d:1: judo uv—fvdu 2 21 a: 1n(5x)_/x__dm H i 2 2 :1: x2 1n(533) a: _ 2 - 5d”: l = x2 1n(5:c) _ it: + C, [\D 4; 1 1 (e) Integrate / a: — 2 dm (3:2 —- 450 + 1)2 Solution: Use u—substitution u=w2—4z+1,du=(2x—4)dx H l / 23—2 d 1/ 293—4 dm (x2—4x+1)2 m 2 (m2—4x+1)2 _1du _2u2 H ml b—l g| w 9.. Q lu—l — 5:” 1 — —%+C — — 1 +0 _ 2(x2—4m+1) 12 Determine of the improper integral converges or diverges. If it converges, evaluate. °° 1 d [0 x2+4$ Solution: °° 1 t 1 = 1' f0 $2+4dx tiglo O x2+4dx _ 1 t x) m=t _ t—Ig2arc an<2 :c=0 — 11 1 t t 1 t (0) — Ergo 2 are an 2 2 are an . 1 t = tljgloéarctan (§)—0 _ 177 _ 22 _ E _ 4 3 ...
View Full Document

This note was uploaded on 03/20/2008 for the course MA 141 and 24 taught by Professor Dempster/mccolum during the Spring '08 term at N.C. State.

Page1 / 8

1ab - MA 241 Test 1 Form E Spnng 9 Set 11 ONLY a b and c...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online