Integration by substitution

Hey,

I am revising from http://pmt.physicsandmathstutor.com/download/Maths/A-level/C4/Worksheets-Notes/OCR%20C4%20Revision%20Notes.pdf at present and did the practice integral of https://www.wolframalpha.com/input/?i=integral+from+3+to+4+2x(x%5E2-4)%5E1%2F2+dx and did it perfectly fine but it seems both aforementioned sources used the original limits instead of the new limits which makes no sense to me as I thought you had to change the limits and use those (which would give an answer of 1,040.2).

Why are they using the original limits of 3 and 4 and not 5 and 12?

Thanks.

Hey,

I am revising from http://pmt.physicsandmathstutor.com/download/Maths/A-level/C4/Worksheets-Notes/OCR%20C4%20Revision%20Notes.pdf at present and did the practice integral of https://www.wolframalpha.com/input/?i=integral+from+3+to+4+2x(x%5E2-4)%5E1%2F2+dx and did it perfectly fine but it seems both aforementioned sources used the original limits instead of the new limits which makes no sense to me as I thought you had to change the limits and use those (which would give an answer of 1,040.2).

Why are they using the original limits of 3 and 4 and not 5 and 12?

Thanks.

Neither source uses the original limits (3 and 4), can explain a bit what you mean?

Neither source uses the original limits (3 and 4), can explain a bit what you mean?

You can use the limits of $x=3$ and $x=4$ if you revert your integrated function $f(u)$ back into $f(x)$