A particle moves along the smooth curve y=f(x) from (a,f(a)) to (b,f(b)). The force moving the particle has constant magnitude k and always points away from the origin. Show that the work done by the force is $\displaystyle \int_{c}F*T ds=k[(b^{2}+(f(b))^{2})^{1/2}-(a^{2}+(f(a))^{2})^{1/2}]$