$\text { The vertical cross section of an irrigation canal is modeled by } f ( x ) = \frac { 5 x ^ { 2 } } { \left( x ^ { 2 } + 4 \right) } \text {, }$

Multiple Choice

$\text { The vertical cross section of an irrigation canal is modeled by } f ( x ) = \frac { 5 x ^ { 2 } } { \left( x ^ { 2 } + 4 \right) } \text {, }$ where $x$ is measured in feet and $x = 0$ corresponds to the center of the canal. Use the integration capabilities of a graphing utility to approximate the fluid force against a vertical gate used to stop the flow of water if the water is 3 feet deep. Round your answer to three decimal places.

A) $307.133 \mathrm { lb }$
B) $546.265 \mathrm { lb }$
C) $356.133 \mathrm { lb }$
D) $707.133 \mathrm { lb }$
E) $1,036.133 \mathrm { lb }$