Integrate sqrt(u-2)

1. Aug 22, 2013

DigiDigi

I was doing a question using u substitution and at one point,I got sqrt(u-2). How do I integrate it further?

Can I integrate is straight away with sqrt(u-2)(2/3) as answer or do I have to use trigonometric substitution? How to do if it's trigonometric?

Last edited: Aug 22, 2013
2. Aug 22, 2013

arildno

Don't bother about the trig substitution. It will hiss at you, just as a nasty and venomous serpent would do.

And if you feel uncertain about integrating straight away, just substitute with the new variable s=u-2, and see where that leads you.

3. Aug 22, 2013

DigiDigi

So,I don't have to use trigonometric substitution?

4. Aug 22, 2013

arildno

Why tread on a rattle snake?
Much easier to substitute v=u-2

5. Aug 22, 2013

DigiDigi

Can I just integrate straight away? I mean I already u-substitution already do I need to do another substitution?

6. Aug 22, 2013

arildno

You never "need" to do any type of substitution. Substitutions are made in order to simplify the problem, but if the problem is simple enough (i.e, you what the answer will be), then there is not much point in further simplification, is there.

However, you expressed an uncertainty as to whether it was "allowed" to integrate straight away. (Everything is allowed to do in maths, provided it is correct. )

In order to alleviate that uncertainty, I pointed out to you that you CAN make the u-2 substition, if that makes you feel safer in doing the right thing.

7. Aug 22, 2013

Staff: Mentor

To elaborate on what arildno said, if you make the substitution v = u - 2, then dv = du, so the integral changes like so:
$$\int \sqrt{u - 2}du = \int \sqrt{v}dv$$

The latter integral is pretty easy. A trig substitution is not needed here, but is very useful if the quantity in the radical is a sum or difference of squares.