Question

Find the area of the surface obtained by rotating the curve x = (1/3)((Y^2) +2)^(3/2), about the x-axis.

Answer 1

\[ \int\limits_{c}^{d}2\pi y \sqrt{1+(\frac{dx}{dy})^2} dy\]

Answer 2

like is the curve bounded by anything?

Answer 3

Sorry yea it is 1< Y <2

Answer 4

ok coolness so what is the problem the integration or the derivative of x with respect to y?

Answer 5

did you get dx/dy yet?

Answer 6

the integral is usually the hard part of these surface area problems

Answer 7

dy/dx is 1/2(y^2 +2)^(1/2) * 2y. Im stuck on how its bounds by 1<y<2 and not x when you're rotating around x axis

Answer 8

Like I'm not saying this is how the curve looks exactly