The stream velocity component of a steady, incompressible, laminar, flat plate boundary layer of boundary layer thickness $\delta$ is approximated by the parabolic expression, $\frac{u}{U} = 2(\frac{y}{\delta}) - (\frac{y}{\delta})^2$ for $y < \delta$, and $u = U$ for $y > \delta$ where, $U$ is the free stream velocity and $y$ is the perpendicular distance from the flat plate surface. Based on this parabolic approximation, generate expressions for the displacement thickness, $\delta^*$ as a function of $\delta$.
