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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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This note was uploaded on 07/31/2013 for the course MATH 42 taught by Professor Butscher,a during the Spring '07 term at Stanford.
 Spring '07
 Butscher,A
 Math, Calculus

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