Midterm Exam 2 Solution Summer 2012 on Calculus - Name PID...

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Name:PID:Circle your section:A01 (11am-12pm)orA02 (12pm-1pm)MATH10B: MIDTERMEXAM2July 26th, 2012Do not turn the page until instructed to begin.Turn off and put away your cell phone.No calculators or any other devices are allowed.You may use one 8.5×11 page of handwritten notes, but no other assistance.Read each question carefully, answer each question completely, & show all of your work.Write your solutions clearly and legibly; no credit will be given for illegible solutions.If any question is not clear, ask for clarification.Good luck!#PointsScore110210310410510E.C.3Σ50
1. Take the following indefinite integrals.(a) (5 points)Z1(2-x)2dx.Doing integration by substitution withu= 2-x, we getdu=-dx, which canbe rewritten asdx= (-1)du. Then doing the substitution,Z1(2-x)2dx=Z1u2(-1)du=-Zu-2du=-u-1-1+C=1u+C=12-x+C(b) (5 points)Zln(x)x2dx.We either use #13 from the table of integrals, or we do integration by parts withu= ln(x)anddv=1x2dx.

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