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20b_03f_qe

# 20b_03f_qe - 20B Quizzes Fall 2003 YOU MUST SHOW YOUR WORK...

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20B Quizzes Fall 2003 Bender YOU MUST SHOW YOUR WORK. Q1. Evaluate the following integrals. Z 8 0 r 2 t dt Z e x +1 dx Q2. (a) Evaluate Z ln t t dt . (b) Evaluate R 2 1 4 x (2 x - 3) 50 dx . (c) Write down an integral for the area of the region enclosed by the three curves y = e x , y = x + 1 , x = 2 . Q3 (a) (8 pts) Evaluate the integrals Z ln x x 2 dx Z π 0 x cos x dx (no trig functions in answer) . (b) (4 pts) Set up, but do not evaluate an integral for the volume obtained by rotating the region between y = x 4 and y = 1 about the line y = - 2. Q4 #1 (6 pts) Determine if the following integrals converge or diverge. Remember to give a reason for your answer. (a) Z 1 - 1 dx x 2 (b) Z 1 dx x 2 . Q4 #2 (6 pts) Estimating R 3 - 1 f ( x ) dx using the Trapezoidal Rule, I obtained T 4 = 8 and T 8 = 5. I also know that | f 0 ( x ) | ≤ 54 and | f 00 ( x ) | ≤ 36 for - 1 x 3. (a) Find a guaranteed bound on the error in T 8 . (b) Find a reasonable estimate for the error in
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