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**billa** 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)***j** where t is between 0 and 2 including 0 and 2

Here is r again

$\displaystyle

r(t) = (\frac{1}

{4}e^{4t} - t){\mathbf{i}} + (e^{2t} ){\mathbf{j}}

$

Here is what I did...

$\displaystyle

V = \int\limits_0^2 {\pi y^2 dx = } \int\limits_0^2 {\pi y^2 \frac{{dx}}

{{dt}}dt = } \int\limits_0^2 {\pi e^{4t} (e^{4t} - 1)dt = } \pi e^{16} - \pi e^8

$

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