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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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