Area of a surface of Revolution

Question

If the infinite curve y= e^-8x, x ≥ 0 is rotated about the x-axis. Find the area of the resulting surface.

Answer 1

s = 2π∫₀^∞e^-8x√1 + 64e^-16xdx; Let tanu = 8e^-8x; sec²udu = - 64e^-8xdx; and will get integral of sec³u, you can

take it by parts.