151reviewfSp09

# 151reviewfSp09 - Math 151 Spring 2009 Review Problems for...

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Math 151, Spring 2009, Review Problems for Final Exam This review sheet emphasizes the material covered after Exam 2. You SHOULD also study the problems in the review sheets for the ﬁrst and second exam. 1. Evaluate the following integrals: (a) Z x 2 4 x + 3 dx (b) Z e - x 1 + e - 2 x dx (c) Z (10 x + 3) 20 dx (d) Z 1 x (ln( x )) 2 dx (e) Z x ( x 4 + 1) dx 2. Evaluate the following integrals: (a) Z 2 - 3 | x 2 + x - 2 | dx (b) Z ln(2) 0 e x e x + 2 dx (c) Z π 4 0 ( tan 3 ( x ) + tan( x ) ) dx (d) Z 2 1 x + 6 x dx 3. Assume f ( x ) is a continuous function on [4 , 7] with the property Z 2 1 f (3 x + 1) dx = 9. Find Z 7 4 f ( x ) dx . 4. Let f ( x ) = ± 4 x + 3 , x < 2 x 3 + x + 1 , x 2 . Find Z 3 0 f ( x ) dx . 5. Evaluate the following derivatives: (a) d dx ² e 2 x ln(4 x ) x + sin - 1 ( x ) ³ (b) d dx tan - 1 ( x + 3 x ) (c) d dx Z x 0 e - t 2 dt (d) d dx Z x - x 1 t 4 + 1 dt (e) d dx p sec( x 2 ) + x 2 + 1 6. Evaluate N X j =0 (3 j + 1) 2 = 1 2 + 4 2 + 7 2 + ··· + (3 N + 1) 2 . 7. Find the left endpoint, midpoint, and right endpoint approximations,

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151reviewfSp09 - Math 151 Spring 2009 Review Problems for...

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