Find the area of a surface of Revolution

[warreneelroy]

the problem is 9x=(y)^(2)+18, 2<x<6.

 

[stapel]

What are you supposed to do with this equation?

Eliz.

 

[warreneelroy]

find the area of a surface of Revolution

you are supposed to find the area of the surface obtained by rotating the curve about the x-axis.
using the formula S= (intergral){a<=x<=b)*(2pi*y)*(sqrt(1+(f '(x))^2)dx

starting with the given, rearrange to: y=3sqrt(x-2), differentiate to get:
f '(x)= 3/(2sqrt(x-2))


so S=integral(2 to 6) (2pi*3sqrt(x-2))*(sqrt(1+9/4(x-2)))dx

The correct answer to this problem is 49pi.

I cannot get this.

thanks for your help!