Please sign the following on my honor i have neither

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Unformatted text preview: s of the submission process. • Please sign the following: “On my honor, I have neither given nor received any aid on this examination. I have furthermore abided by all other aspects of the honor code with respect to this examination.” Signature: The following boxes are strictly for grading purposes. Please do not mark. 1 40 5 8 2 8 6 10 3 10 7 8 4 8 8 8 Total 100 Math 42, Winter 2010 First Exam — January 28, 2010 1. (40 points) Evaluate each of the following integrals, showing all of your reasoning. 8 (a) √ x 1 + x dx 3 (b) et cos t dt Page 1 of 11 Math 42, Winter 2010 x2 (c) ∞ (d) 1 9 − x2 dx √ e− √ x x dx First Exam — January 28, 2010 Page 2 of 11 Math 42, Winter 2010 (e) 1 √ √ dt (t + 2 t + 2) t First Exam — January 28, 2010 Page 3 of 11 Math 42, Winter 2010 (f) x3 2x2 dx = − x2 − x + 1 First Exam — January 28, 2010 2x2 dx (x − 1)2 (x + 1) Page 4 of 11 Math 42, Winter 2010 First Exam — January 28, 2010 Page 5 of 11 2. (8 points) (a) Set up an integral that represents the length of the curve y = e2x + 3 from the point (0, 4) to the point (1, 3 + e2 ). Show your steps, but stop before evaluating the integral. (b) Now evaluate the integral you found in part (a); you do not have to simplify the numerical expression you obtain. You may find it useful to know the following integral table entry, which you do not have to prove: √ a2 + u2 du = u a2 + u2 − a ln a+ √ a2 + u2 +C u Math 42, Winter 2010...
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