Integration By Substitution

[Guest]

Hello, I have an integration by substitution to do for my homework, but this counts towards whether or not I get onto my course of choice so I would prefer not to have the answer :wink:
Any pointers on what type of substitution I need to make would be appreciated.

$\displaystyle \int_{0}^{4}{1/(1+sqrt{x})}\,dx$

Question says: Use suitable substitutions to evaluate.
So I it's probably sinh, cos or tan?
Thanks
Josh

 

[tkhunny]

You should get to the h-Tangent, but that probably isn't first on your list.

Try $\displaystyle u\,=\,1\,+\,\sqrt{x}$

Noting that: $\displaystyle \sqrt{x}\,=\,u\,-\,1$

That should get you on your way.

 

[Guest]

Thank you very much, I wittled the answer to:
\(\displaystyle \2[u-log{u}]_{1}^{3}\\)
Is that ok?
Cheers again

 

[tkhunny]

No good.

You changed variables. The limits can't be the same. You must change those, too. You have x-limits. You need u-limits.

 

[Guest]

I know, I was putting it on paper and realised :lol: then I started fiddleing around with the LaTex, it's really cool!
Thanks for the help
Josh

 

[tkhunny]

Where's the tanh?

 

[galactus]

You could let $\displaystyle x=u^{2}$and$\displaystyle dx=2udu$

$\displaystyle \int\frac{2u}{1+sqrt{u^{2}}}du$

$\displaystyle \int\frac{2u}{1+u}du$

\(\displaystyle \int\(2-\frac{2}{u+1})du\)