Parametric equations to find surface area

[PsychonautQQ]

Homework Statement

Which of the following integrals represents the area of the surface obtained by rotating the parametric curve
x=t-t^2
y=(4/3)t^(3/2)
1<t<2

Homework Equations

A = integral ( 2pi(y) * sqrt( 1+ (dy/dx)^2))dx

The Attempt at a Solution

I solved for dy/dx and got
12(t^1/2) / (9-18t)
and then plug (1-2t)dt in for dx
and (4/3)t^3/2 for y

If i plug these all in and algebra correctly will i get the correct answer?
How do i include the information that it's being rotated around the x-axis into my equation?

 

[mfb]

If i plug these all in and algebra correctly will i get the correct answer?

That should give the right answer. You can simplify your dy/dx, by the way.

How do i include the information that it's being rotated around the x-axis into my equation?

Your equation at (2.) takes care about that.