20B QuizzesFall 2003BenderYOU MUST SHOW YOUR WORK.Q1. Evaluate the following integrals.Z80r2tdtZex+1dxQ2. (a) EvaluateZlnttdt.(b) EvaluateR214x(2x-3)50dx.(c) Write down an integral for the area of the region enclosed by the three curvesy=ex,y=x+ 1,x= 2.Q3 (a) (8 pts) Evaluate the integralsZlnxx2dxZπ0xcosx dx(no trig functions in answer).(b) (4 pts) Set up, butdo not evaluatean integral for the volume obtained byrotating the region betweeny=x4andy= 1 about the liney=-2.Q4 #1 (6 pts) Determine if the following integrals converge or diverge.Remember togive a reason for your answer.(a)Z1-1dxx2(b)Z∞1dxx2.Q4 #2 (6 pts) EstimatingR3-1f(x)dxusing the Trapezoidal Rule, I obtainedT4= 8 andT8= 5. I also know that|f0(x)| ≤54 and|f00(x)| ≤36 for-1≤x≤3.(a) Find a guaranteed bound on the error inT8.(b) Find a reasonable estimate for the error in
This is the end of the preview.
access the rest of the document.