If the infinite curve y = e-9x, x ≥ 0, is rotated about the x-axis, find the area of the resulting surface.

We are given with the equation

y = e^-9x with the restriction of x ≥ 0

If rotated about the x-axis the area of the resulting surface is

A = π ∫ y² dx

Substituing

A = π ∫ (e^-9x) ² dx

A = π ∫ e^-18x dx

The limits are from 0 to positive infinity.