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## Homework Statement

Find the area of the surface obtained by rotating the curve y=x

^{3}, 0≤x≤2 about the x-axis.

## Homework Equations

\begin{equation*}

SA = \int_{0}^{2} 2 \pi y L

\end{equation*}

## The Attempt at a Solution

SORRY, I don't know how to use LaTeX yet.

∫2∏y√(1+(dy/dx)

^{2})dx from 0->2

=∫2∏y√(1+(3x

^{2})

^{2})dx

=2∏∫x

^{3}√(1+9x

^{4})dx

=2∏∫x

^{3}(1+3x

^{2})dx

=2∏∫x

^{3}+3x

^{5}dx

=2∏[x

^{4}/4 + x

^{6}/2] 0->2

=plug in 2

=72∏

I don't see where I went wrong. The answer is ∏/27*(145√(145)-1)