IF THE INFINITE CURVE yex x from zero to infinity IS ROTATED

Solution

For a thin slab with the width of dx, the slab of surface would be a ring of the radius e^(-x), and its surface is the perimeter of the ring multiplied by the width dx: dA = pi*(e^(-x))^2 * dx = pi * e^(-2x) dx integrate that from 0 to infinity: int. (pi * e^(-2x) dx) = -pi * e^(-x) / 2 Plug in the limits, and you will get the result: pi/2