Volume of Perpendicular Slices for Region Bounded by y=e^x and x=1

[ada0713]

finding volume by integration

Homework Statement

Consider the region bounded by y=e^x, the x-axis, the y-axis, and the line x = 1. A solid is created so that the given region is its base and cross-sections perpendicular to the x-axis are squares. What is the volume of a slice perpendicular to the x-axis?

The Attempt at a Solution

since the regions is bounde by y=e^2, y=0. and x=1,
doesn't the volume of a slice perpendicular to the x-axis
has to be (e^x)(e^x)dx ..(since the base and height are equal)

so the answer should be [Integral from 0 to 1](e^(2x)) dx


Am I wrong? I thought I set it up right but the webassign thing's
keel saying that somethings wrong

I'm in a hurry so please help!
amd

 

[Dick]

That looks correct to me.