math_172_(fall_2008)_(schumaker)_make-up_exam1_(spring08)_solutions

Math_172_(fall_2008)_(schumaker)_make-up_exam1_(spring08)_solutions

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Unformatted text preview: Math 172: Second Semester Calculus Spring Semester, 2008 Make-up Exam 1 nun—an ------_Ifl Ill-II- Name: E % Section: ID Number: Instructions: Work must be shown to receive credit. No calculators. Question 1. (13 points) Find the area of the region bounded by the curve 1 y=— andthelines y=x and x=2. flzlx‘ Owl 13% L Lexi-27:, =7< ”)Ctil 1.0 3.0 Question 2. (15 points) The region R is bounded by the curve y = 1/x where x ranges from 1 to 3 and the x axis. Find the volume of the solid object obtained by rotating R about the xaxis. Question 3 (15 points) The region R is bounded by the curve y = sin x where x ranges from 0 to rr and the x axis. Find the volume of the solid object obtained by rotating R about the y axis. Question 4. (6 points each) Evaluate the following integrals (A) Itan(x)sec3(x)dx . . I [1,: <3er 23$sz mxsecxplx 0m: mxsemogx :Sufdm = Jgu3+C 2 3i38637c+ C 2 (B) I (x+ 3)(x—5) dx :; ”‘V‘I- ‘/ 5‘ 7m“ + :33) 4X :adggdm flx-‘gAx 7t /2 (C) J£COS(2x)dx 0“ Av Question 5. (15 points) Evaluate the following integral - __ ‘ (—31: ‘ t “"6 (9 ”SMmewhéei‘Ms Ch 33% ,_.._ . 321 ~ 1+ x :33 0+ Wm ' 33936 M . ~3/i 3 . 3 59,619 d0 8W“? ,_.. ”)C Q A] (H)?- Question 6. (6 points each) Express the following improper integrals as the appropriate limits. Are they convergent or divergent? lf divergent, explain why. If convergent, evaluate. 1 l ‘ A (A)(j);117§dx:th Wzkgix dx ...
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