the equation is . I found that x=sqrt(1-y) and that x'=-1/(2*sqrt(y-1)).
I've been using integral(2*pi*x*sqrt(1+x'^2)) but i keep just getting mixed up with my calculations.
help would be appreciated.
If you rotate this function about the y-axis, each cross-section parallel to the x-axis will be a circle. The circumference of each circle is $\displaystyle \displaystyle \begin{align*} 2\pi r = 2\pi x = 2\pi \, \sqrt{ 1 - y } \end{align*}$, and if you add up all these circumferences over $\displaystyle \displaystyle \begin{align*} 0 \leq y \leq 1 \end{align*}$ then you will get the total surface area. So
$\displaystyle \displaystyle \begin{align*} SA &= \int_0^1{2\pi \, \sqrt{ 1 - y} \, dy} \end{align*}$