Suppose we have a uniform beam that is $2\mathrm{.}25$ metres long has a flexural rigidity of $32545N{m}^2.$

Find the deflection of the beam in millimetres if the beam is under a load of $f(x)=9\mathrm{.}21(x+2\mathrm{.}24)(2\mathrm{.}42-x)\frac{N}{m}$ and is supported with fixed supports at both ends. Fill out the table below with your answers.

$x-$coordinate

$x=0\mathrm{.}09,y(x)=$

$x=0\mathrm{.}50,y(x)=$

$x=1\mathrm{.}08,y(x)=$

$x=1\mathrm{.}69,y(x)=$

$x=2\mathrm{.}05,y(x)=$

Deflection $(mm)$

$$

Enter as many decimal places as your calculator allows $(8$ to $10).$ Your answer must be within $+-0\mathrm{.}0005$ of the correct answer to be considered correct.