# Thread: Can someone help with this integral--I have tried everything I can think of

1. ## Can someone help with this integral--I have tried everything I can think of

integral sqrt(18x-x^2) dx

I completed the square so now I have
integral sqrt(81-(x-9)^2) dx

u=x-9
du=dx

so now I have integral sqrt(81-u^2) du

and this is where I get lost. I see that there is a sin in there because 81 is 9^2

so should it be u=a cos theta?

2. Originally Posted by operaphantom2003
integral sqrt(18x-x^2) dx

I completed the square so now I have
integral sqrt(81-(x-9)^2) dx

u=x-9
du=dx

so now I have integral sqrt(81-u^2) du

and this is where I get lost. I see that there is a sin in there because 81 is 9^2

so should it be u=a cos theta?
$\int\sqrt{18x-x^2}\,dx=\int\sqrt{81-(x-9)^2}\,dx$

I would recommend the trigonometric substitution $x-9=9\sin\theta$.

Can you try it from here?