fall02 Integral Ans

Thomas' Calculus: Early Transcendentals

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Unformatted text preview: Mat104 Fall 2002, Integration Problems From Old Exams Warning: Many of these integrals can be done several different ways. If you choose a different method than I did, your answer may look quite different from the answer given here. The two different-looking answers may simply differ by a constant or perhaps they can be seen to be the same through the clever use of identities. If you believe that your answer is correct, but it does not match the one given here, consult your instructor! If you find errors, please let me know ([email protected]). (1) cos 2 x- cos 4 x 4 + ln | sec x | + C (2) 1 16 x √ 4 + x 2- 1 48 · x 3 ( √ 4 + x 2 ) 3 + C (3)- 2 √ 1 + x cos √ 1 + x + 2 sin √ 1 + x + C (4) x arctan x- ln √ 1 + x 2 + C (5) 3 x 8 + sin 2 x 4 + sin 4 x 32 + C or, equivalently, 3 x 8 + cos 3 x sin x 4 + 3 8 cos x sin x + C (6) 1 4 ln 3 (7) ln(1 + ln x ) + (ln x ) ln(1 + ln x )- ln x + C (8) x 3 arctan x 3- x 2 6 + ln √ 1 + x 2 3 + C (9) 1 8 √ 3 (10) e x 2 4 (sin x 2...
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fall02 Integral Ans - Mat104 Fall 2002 Integration Problems...

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