Question

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

Answer 1

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.