Integrating the left hand side of the equation $\int K(p) dp$, using the methods of sections 7.3 and 7.3, we obtain
$\int K(p) dp$ =
while on the right hand side we obtain $\int L(x) dx$ = $+C$

Plugging in the initial positions of the hawk and pigeon, and recalling that $p=\frac{dy}{dx}$ is the slope of the tangent line, we find that
$C$ =