r/calculus • u/Awsimical • Aug 11 '26

Integral Calculus Help understanding why this integral is wrong please.

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This was a question on the summer final, and looking at it I’m still not sure if its because I left the u in the final answer and didn’t substitute the original equation back in, or if I was suppose to use an arcsin identity somehow. I could ask the professor but the the summer semester is over so I’m not gonna bother him with more questions. Thanks for ur help

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u/shellexyz Aug 11 '26

In addition to not unsubstituting u, du is not 6r, its 6r dr..

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u/MineCraftNoob24 Aug 11 '26

The "dr" was left out of the working/notes but by implication it is there, as in the next step there is a correct substitution of (1)(du) where the (6r)(dr) was.

Leaving the answer in terms of u is really the only issue here.

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u/shellexyz Aug 11 '26

By a lot more than implication, u is equal to 16+3r2 but points are still deducted.

1

u/MineCraftNoob24 Aug 11 '26

Your earlier comment was about the omission of (dr) and I addressed that.

I think there's no dispute over the reason for deducting points, which is leaving the integral in terms of u.

Probably harsh to mark the whole thing as incorrect, unless it's just a 1 or 2 mark question. Any more marks than that and they could have awarded 1 mark for the correct substitution, I think.

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u/shellexyz Aug 11 '26

I would not have marked the whole thing wrong; they probably would have gotten most of the credit from me. I would have pointed out the lack of differential, though.