Find the area of the surface obtained by rotating the curve about the $x$-axis.
$$x = \frac { 1 } { 3 } \left( y ^ { 2 } + 2 \right) ^ { \frac { 3 } { 2 } } , 1 \leq y \leq 4$$

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The Answer of Find the area of the surface obtained by rotating the curve about the $x$-axis.
$$x = \frac { 1 } { 3 } \left( y ^ { 2 } + 2 \right) ^ { \frac { 3 } { 2 } } , 1 \leq y \leq 4$$

Find the Area of the Surface Obtained by Rotating the Curve