Hey,

What is the best approach to integrate this:

sqrt[ (t+a)^2 + a^2 ] dt

Thanks in advance (Happy)

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- Jan 9th 2011, 07:17 AMfatluckyIntegration approaches
Hey,

What is the best approach to integrate this:

sqrt[ (t+a)^2 + a^2 ] dt

Thanks in advance (Happy) - Jan 9th 2011, 07:28 AMalexmahone
- Jan 9th 2011, 07:32 AMRandom Variable
First let $\displaystyle u = t+a $. The let $\displaystyle u = a \tan x $

- Jan 9th 2011, 07:42 AMTheCoffeeMachine
Put $\displaystyle (t+a) = a\sinh{\varphi}$.

- Jan 9th 2011, 07:55 AMfatlucky
Damn.. I was thinking there would be a more obvious substitution I could use..

I would not think to use these in a calculus exam :O

Thanks for the suggestions - I'll be trying them out now and see what works best for me :D - Jan 9th 2011, 08:15 AMchisigma
In my opinion the best way is the simple substution $\displaystyle x= \frac{t}{a}$ so that the integral becomes...

$\displaystyle \displaystyle a^{2}\ \int \sqrt{1+ x^{2}}\ dx$ (1)

... that can be solved by parts in some steps...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$