math_172_(fall_2008)_(schumaker)_first_exam_(spring07)_solutions

# Math_172_(fall_2008)_(schumaker)_first_exam_(spring07)_solutions

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Unformatted text preview: Math 172: Second Semester Calculus Spring Semester, 2007 First Exam “Hum III-II- Name: ' Section: ID Number: Instructions: Work must be shown to receive credit. No calculators. Question 1. (15 points) Find the area of the region enclosed by the curvesy=3—xandy=2/x. " In‘i‘eVSecl‘lomS? - 3~x> Z/)< I‘n ewclowgl “23".” Question 2. (5 points each) Compute the following integrals. (A) jx1n(x)dx :- I ‘ IBIZA/x} (B) Isec2(x)tan3(x)dx :. J \T; f Sec/(1)10442/X) IGC/X} Tim/X) dx = f Maw/{eB/M- I) rec/2c) tan/009‘ 'M= Alt/X) Au: Mc/)()En/1)JOL x +2x ( - 14 i x/x+z) “ ; X+L I I ~ Z R I: A/X+Z)+ EX y I: if! / 7‘_x+2_)d)( = /= ’42 I? ’4: 1- . z X 0)) /: ~22 1571 I ZIMA’X/‘ﬂw/“ZWI )(s‘z _— EVA/2)sz [4) V (D) xzsin(x)dx :J’ _[ﬂﬂ/1)_.ﬂ'/3)) U: X’- dv:rm/Z) dar— : (Z)‘Z.ZJZJ+/m L?» du= Zxdx V: “cor/X) , K - l I “z _x2cos(x) +f2xau/x2clz I - Z l3)-L/ZJ) . /(= Ix cos/xh‘X K = X W“) —/5‘M Ma’x u;x dv=comodx ="er/XJ.,L [of/,9) +5 (JM: Jx V: 940‘) : “Xzf‘J/X) +2xr/a/x)+ 2co://VJ+D Question 3. (10 points) Use any method to evaluate the indefinite integral Edi/est” [I Joi>fh¥u+lng I: Ifmdx I = f gyms) Zm/eNIaS/eMe 32 f 5153/9) (0:249) 49 .- ’ ‘szﬂ/I—au%eﬂsz9?ﬂw%N9 [3+ AA= 645(9) 1 edu) 1‘: .: Ezra/{H‘M/22du‘ -1 3 + : 32— (éwsgu) C Question 4. (5 points each) Evaluate the following improper integrals, indicating if any of them diverges. For full credit, any improper integral must be re-interpreted as an appropriate limit. so - ‘ ‘t .. A) L = I ‘ V’mf/ ch/X Question 5. (20 points) Let R be the region bounded by x = 0, x = 1, y = x2 + 1 and the x—axis. * x — axis. 1 [I 0 _— rz/éX‘r1‘gng’é Xj/o/ - rz/fl“§+’) C ﬂ/g-{FJ—IO‘P‘I: - if”. Question 6. (20 points) Let R be the same region as in question 5, Le. bounded by x = 0, x = 1, y = x? + 1 and the x-axis. Find the volume of the object obtained by spinning R about the y - axis. - 77w MtiﬂL Mad 2: 9/1111»le {Leaf __th' a/yp/I‘Caéza ‘fd 0W MW. ...
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## This note was uploaded on 02/14/2011 for the course MATH 172 taught by Professor Remaley during the Spring '10 term at Washington State University .

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Math_172_(fall_2008)_(schumaker)_first_exam_(spring07)_solutions

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