Integrating (2rx - x2)1/2 w.r.t. x and Constant r

[fysiikka111]

Homework Statement

Integrate
(2rx-x²)^1/2
with respect to x where r is a constant.

Homework Equations

The Attempt at a Solution

Thanks

 

[micromass]

What did you attempt already?

 

[fysiikka111]

Integration by substitution.

 

[micromass]

what substitution did you try?

 

[fysiikka111]

cos(x) to see if I could then use a trig identity.

 

[micromass]

Did you try to complete the square?

 

[fysiikka111]

so
(2rx-x²)^1/2=(r²-(x-r)²)^1/2

 

[micromass]

Yes, so now it should be a lot easier...

 

[fysiikka111]

I'm not sure what substitution to use.

 

[dextercioby]

x-r = r cos t ??

 

[fysiikka111]

That worked, thanks a lot.