midterm2 - 1 1 x 2-1 dx (hint: R sec u du = ln | sec u +...

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CALCULUS 153: MIDTERM 2 Please answer all questions in a blue book that’s provided to you. Don’t forget to write your name. There are two sides to this exam. Problem 1 (32 points) . Compute the following integrals (8 points each) (a) Z tan x sin 2 x dx (b) Z dx x 2 - 4 x + 5 (c) Z arctan x dx (d) Z x + 1 x 2 - 2 x + 1 dx. Problem 2 (20 points) . (a) Find the general solution of y 0 = 2 xe - y and the particular solution when y (0) = 1 (10 points). (b) Find the general solution of y 0 = y + e x and the particular solution when y (0) = 1 (10 points). Problem 3 (20 points) . Calculate the following integrals (10 points each). (a) Z 2
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Unformatted text preview: 1 1 x 2-1 dx (hint: R sec u du = ln | sec u + tan u | + C .) (b) Z 2 dx x ln x Problem 4 (16 points) . Use the comparison test to determine whether the following integral converge or diverge. Note that you do not need to evaluate the integrals (8 points each). 1 2 CALCULUS 153: MIDTERM 2 (a) Z 1 ln x x 2 dx. (b) Z e ln x x 2-1 dx. Problem 5 (12 points) . Suppose that f ( a ) = f ( b ) = g ( a ) = g ( b ) = 0. Show that Z b a f ( x ) g 00 ( x ) dx = Z b a g ( x ) f 00 ( x ) dx....
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midterm2 - 1 1 x 2-1 dx (hint: R sec u du = ln | sec u +...

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