Integration: Washer and shell method

[Bryon]

Hi Everyone

I am having a trouble setting up an equation: I am to find the volume by integrating the equation y = 4-e^x from 0 to 3 and rotate it about the axis of x = 10.

Here is what I have:

the equation y= 4-e^x in terms of x is x = ln(4-y)


R(y) = 10
r(y) = ln(4-y)

the equation I have using the disk method is this:

v = 2pi integrate from 0 to 3 (10^2)-(ln(4-y))^2)dy

using the shell method I have (which I think is correct):

v = 2pi integrate from 0 to ln4 (10-x)(4-e^x)dx

 

[Bryon]

Wait...I figured it out.