Question

Help:
Surface area when the arc of y = e^-x, x>=0 is rotated about the x-axis

What I did:
y = 1/(e^x)
dy/dx = -e^(-x)
substitute in
S = 2pi integral(from 0 to infinity) (y)(sqrt(1+(y')^2))dx

So..
S = 2pi int_0^(inf) (e^(-x))(sqrt( 1 + (-e^(-x))^2)dx
is this right?