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 %3 u? +С 3 sin? x +C. Bob made the substitution u = cosx with du =- sinxdx, and then wrote: 2 sinxcos.xdx = /: 2 cosx (sinxdx) 2u (-du) — — и? +С%3- сos? х+С. = 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"?
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 %3 u? +С 3 sin? x +C. Bob made the substitution u = cosx with du =- sinxdx, and then wrote: 2 sinxcos.xdx = /: 2 cosx (sinxdx) 2u (-du) — — и? +С%3- сos? х+С. = 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"?
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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