Find the area of the surface generated by revolving the curve about the indicated axis.
y= squareroot(5x-x^2), 0.5

Question

Find the area of the surface generated by revolving the curve about the indicated axis. 
 y= squareroot(5x-x^2),  0.5 <= x <= 1.5, x-axis

How would I set up this integral?  I know the formula but how would the integral look?

tkhunny · Answer

1) Find limits of integration.  These are given x is [½.1½].  y is a little trickier, but without much difficulty, we see $\left[\dfrac{3}{2},\dfrac{\sqrt{21}}{2}\right]$

2) Decide Disks or Shells.  It doesn't much matter in this particular problem.  Pick your favorite.

anonymous · Answer

I got 5Pi is that correct?

anonymous · Answer

does anyone know if 5Pi is the answer for this?

tkhunny · Answer

Yes.  That is the right answer.  Did you get it by luck?

anonymous · Answer

I think so..  I set up my integral and then entered it into my calculator.  So 5pi is correct?  Thank you for your help

tkhunny · Answer

It's a wonderful algebra exercise.  The square root is quite a mess, but the function has just what is needed to clean it up.

Good work.

anonymous · Answer

Thanks again! I have another problem I am going to post up if you want to help you are more than welcome! lol