A uniform beam forms the semiparabolic cantilever arch $AB.$ The vertical displacement of A due to the force $P$ can be shown to be

${}_A=\frac{P*b^3}{EI}C(\frac{h}{b})$

where EI is the bending rigidity of the beam and

$C(\frac{h}{b})={\displaystyle \underset{0}{\overset{1}{}}}{z}^2\sqrt[\phantom{2}]{1+(\frac{2h}{b}z{)}^2}dz$

Compute $C(0\mathrm{.}5),C(1\mathrm{.}0)$ and $C(2\mathrm{.}0).$ Use all methods that apply to the problem. You can use computer software as Matlab user$-$defined functions. Compare results and rank methods from best to worse.