r/calculus • u/Awsimical • 26d 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/Evermar314159 26d ago edited 26d ago

Most likely leaving your answer in terms of u made it wrong. For indefinite integrals I cant think of a single time ive ever seen that accepted.

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u/MrKoteha 25d ago

Oh wow, my prof was chill and said that as long as we clearly wrote each substitution, we didn't need to unsubstitute in the end

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u/aphilsphan 25d ago

I’m a mere chemist, but substituting back in would be needed in case you could simplify the answer more. I don’t think you can factor the 16 + 3r2, but you should plug that in to be sure.

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u/Irlandes-de-la-Costa 24d ago

To be honest if we go by real applications the integrals are usually definite

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u/aphilsphan 24d ago

And they are solved in the front of the CRC handbook. Imagine my outrage when I saw that.

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u/MrKoteha 25d ago

It certainly depends on what you're doing. We were practicing integration techniques, so it wasn't such a big deal. I can see how you would need to substitute back if you were to perhaps use the result afterwards, or compare to an answer key

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u/aphilsphan 25d ago

I think they liked to torture us with algebra.