IF THE INFINITE CURVE yex when x is greater or equal to zero

IF THE INFINITE CURVE y=e^(-x), when x is greater or equal to zero

IS ROTATED ABOUT THE X-AXIS, FIND THE SURFACE AREA.

*MAKE SURE TO SHOW ALL WORK

Solution

Curve = e^(-x) height at any point = e^(-x) circumference at any x = 2piy = 2pi(e^(-x) integrating this from 0 to infinity gives surface area = integral 2pi*e^(-x)dx from 0 to infinity = -2pi*e^(-x) +c from 0 to infinity = 2pi sorry if i gave wrong answer previously