Find the volume of the solid created by revolving the curve C about the x-axis. C is defined by the curve r(t)=[(.25)e^(4t)-t]*i+ e^(2t)*jwhere t is between 0 and 2 including 0 and 2

Here is r again

Here is what I did...

Is this right? I have no answer key so I have no way to check. Thanks