Question

Find the surface area of the unbounded surface formed by revolving the graph of y=e^-x, for x is greater than or equal to 0 about the x-axis. Please show work of how you got the answer.

Answer 1

The surface area is basically a sum of the circumferences of each circle, so
\[A=\int_0^\infty P(x)~dS\]
where \(dS=\sqrt{1+\left(\dfrac{dy}{dx}\right)^2}~dx\)