- #1
Saterial
- 54
- 0
Homework Statement
Find the area of the surface obtained by rotating the curve y=x3, 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+(3x2)2)dx
=2∏∫x3√(1+9x4)dx
=2∏∫x3(1+3x2)dx
=2∏∫x3+3x5dx
=2∏[x4/4 + x6/2] 0->2
=plug in 2
=72∏
I don't see where I went wrong. The answer is ∏/27*(145√(145)-1)