CalcAnswersCh5

CalcAnswersCh5 - (Answers to Exercises for Chapter 5:...

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(Answers to Exercises for Chapter 5: Integrals) A.5.1 CHAPTER 5: INTEGRALS SECTION 5.1: ANTIDERIVATIVES and INDEFINITE INTEGRALS 1) a) x 4 2 ± 4 x 7/4 35 ± x 6 12 + 4 x 3 ± 3 x + C , or 1 2 x 4 ± 4 35 xx 3 4 () ± 1 12 x 6 + 4 3 x ± 3 x + C . (Note: Many books don’t even mention that we require x > 0 in the given exercise, even though that restriction is not fully evident in the answer.) b) 2 y 5/2 5 + C , or 2 5 y 2 y + C (Note: The restriction y ± 0 is evident in the answer here.) c) t 3 ± t 2 + 2 + C . (Note: We technically require: t > 0 .) d) w 3 3 + 7 w 2 2 + 12 w + C , or 1 3 w 3 + 7 2 w 2 + 12 w + C e) 81 z 5 5 + C , or 81 5 z 5 + C f) ± 1 t ± 2 t 3 ± 9 5 t 5 + C , or C ± 1 t ± 2 t 3 ± 9 5 t 5 , or C ± 5 t 4 + 10 t 2 + 9 5 t 5 g) x 3 3 ± x 2 + 4 x + C . (Note: We technically require: x ±² 2 .) Hint: Factor the numerator. h) ± 3cos x + 5sin x + C , or C ± 3cos x + x i) 4tan ± + C j) ± cot t + C , or C ± cot t . (Note: We technically require : cos t ± 0 . The restriction sin t ± 0 is essentially evident in the answer.)
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(Answers to Exercises for Chapter 5: Integrals) A.5.2 k) sec r + C . l) ± csc ² + C , or C ± csc . Hint: Use a Pythagorean Identity.
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This note was uploaded on 09/08/2011 for the course MATH 150 taught by Professor Bart during the Spring '06 term at Mesa CC.

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CalcAnswersCh5 - (Answers to Exercises for Chapter 5:...

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