The +C still doesn't matter, since the results only differ by a constant ... 1.
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You literally just argued why the constant matters
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I prefer another way for solving this without substitution. just write it as ½∫2sin(x)cos(x)dx = ½∫sin(2x)dx. Solving this gives "-¼cos(2x)," which also differs from the above two by a constant.pic.twitter.com/K2bmAZGwF9
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very nice
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I basically agree with your student. Writing +C for every indefinite integral is a waste of ink.
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On an exam you need to demonstrate you know it should be there.
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I don't agree with the student here but I do believe that we hammer "+C" into students in kind of a silly way. I bet there isn't a strong correlation between understanding why & remembering to write it. I do like asking them questions like "wtf is happening in [your post]" though
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agree 100%
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It shouldn’t be the equality at the first place. The indefinite integral is like a set of functions. It’s more of a belonging-to relationship.
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that's the point
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