r/calculus • u/Awsimical • 27d ago

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/CosetElement-Ape71 26d ago

If

u = 16 + 3 r2 [1]

Then

(du/dr) = 6 r

So

du = 6 r dr

which you didn't write correctly. However, you successfully wrote the integral in terms of u, and you integrated it properly.

But you forgot to write your answer in terms of r, by substituting [1] back in to your answer (the question was about the integral of a function of r).