A robotic arm's force output $F$, in Newtons, is modeled by $F(x)=x\sqrt{2x-1}$ where $x$ is the extension in metres. Use integration by substitution to show that the total work done $W$ during an extension from $x=\frac{1}{2}$ to $x=4$ is given by

$$W={\int }_{\frac{1}{2}}^{4}x\sqrt{2x-1}dx=\frac{91\sqrt{7}}{15}$$

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