Find the Volume of the Resulting Solid If the Region $y = \frac { 1 } { \left( x ^ { 2 } + 3 x + 2 \right) }$

Short Answer

Find the volume of the resulting solid if the region under the curve $y = \frac { 1 } { \left( x ^ { 2 } + 3 x + 2 \right) }$ from $x = 0$ to $x = 1$ is rotated about the $x$ -axis. Round your answer to four decimal places.