Question

can anyone give me a few tips on using u substitution when evaluating definite integrals?

Answer 1

\[\int\limits_{1}^{4}\sqrt{\frac{ 9y+1 }{ 9y }}dy\]

Answer 2

This is the specific problem I am working on for the moment but I am looking for some tips in general that will help me decide what to make u

Answer 3

man i used to be so good at this... hang on a sec

Answer 4

Well for starters I'd pull out whatever i can, so:
\[(1/3)\int(\sqrt{(9y+1)/y}dy\]

Answer 5

Now I don't really see any options other than setting u=(9y+1)/y

Answer 6

du would then be u'=((9y+1)y^(-1))' = (9y^(-1)) - (9y+1)y^(-2)