Exam_exam_2_

# Exam_exam_2_ - a b ±or n = 10 and the integral R 8-2 1 x 3...

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MIDTERM 2 — MATH 141 — SPRING 2003 — BOYLE Use exactly ONE answer sheet per question (use the back of the sheet if needed). Put your name, your TA’s name and the question number on EACH page. Put a BOX around the Fnal answer to a question. No books, no notes, no calculators. Before handing in your test: on your Frst answer sheet, please copy the pledge, and sign. ———————————————————————————————————– 1 (a) (20 points) Compute the integral R tan 7 x sec 4 x dx . (b) (10 points) Let S n denote the Simpson’s Rule estimate for a given R b a f ( x ) dx and let E n = | S n - R b a f ( x ) dx | . Then we have a bound E n B n , where B n = ( b - a ) 5 180 (max | f ( iv ) | ) 1 n 4 where the maximum is taken over the interval [
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Unformatted text preview: a, b ]. ±or n = 10 and the integral R 8-2 1 / ( x + 3), compute the bound B n . 2 (20 points) Compute the integral Z x 2 + x + 4 ( x-1) 2 ( x + 1) dx 3 . (20 points) Compute the following integral. Z log 4 ( x ) dx 4 (a) (15 points) Compute the following improper integral. Z ∞-∞ 1 x 2 + 2 x + 17 dx (b) (15 points) ±or each integral below, give the appropriate description: ∞ ;-∞ ; DNE (does not exist); or CONVERGES (i.e. the improper integral is well deFned and converges to a Fnite real number–you don’t have to compute it). No proof required. ( a ) Z 1 1 x ln( x ) dx ( b ) Z 1-1 1 x dx ( c ) Z ∞ 1 e-x 2 dx...
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