Volume of region roated about specified axi

[Painguy]

Homework Statement

y = e^(-x), y = 0, x = -1, x = 0, about x = 1

Homework Equations

The Attempt at a Solution

2pi∫ (1-x)(e^(-x) dx from -1 to 0

=2pi∫ e^(-x) -x*e^(-x) dx from -1 to 0
=2pi(-e^(-x) - ∫x*e^(-x) dx from -1 to 0
u=x
du=dx
dv=e^(-x)dx
v=-e^(-x)
2pi(-e^(-x)-(-xe^(-x) +∫e^(-x)dx))
2pi(-e^(-x) +xe^(-x) +e^(-x))
2pi(xe^(-x)) from -1 to 0
2pi(e)

is this right?

 

[Dick]

Seems ok to me.