Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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3. You are working with your friends Alice and Bob on your Calculus homework. While you were away running an errand, they computed the integral / 2 sinxcosxdx, but they cannot agree on the correct answer. Alice made the substitution u = sinx with du = cosxdx, and then wrote: 2 sinxcosxdx = | 2 sinx(cos.xdx) = / 2udu = u? +C = sin?x+C. Bob made the substitution u = cosx with du = – sinxdx, and then wrote: 2 sinxcosxdx = | 2cosx (sinxdx) = | 2u(-du) = -ư² +C=- cos?x+C. Did one of your friends make a mistake? If yes, who made a mistake and where is the mistake? If you think neither of them made a mistake, then address their concern:"How can you have two different-looking correct answers for the same integral"?
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Transcribed Image Text:3. You are working with your friends Alice and Bob on your Calculus homework. While you were away running an errand, they computed the integral / 2 sinxcosxdx, but they cannot agree on the correct answer. Alice made the substitution u = sinx with du = cosxdx, and then wrote: 2 sinxcosxdx = | 2 sinx(cos.xdx) = / 2udu = u? +C = sin?x+C. Bob made the substitution u = cosx with du = – sinxdx, and then wrote: 2 sinxcosxdx = | 2cosx (sinxdx) = | 2u(-du) = -ư² +C=- cos?x+C. Did one of your friends make a mistake? If yes, who made a mistake and where is the mistake? If you think neither of them made a mistake, then address their concern:"How can you have two different-looking correct answers for the same integral"?
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