$(4)$ Cantilever beam $AB$ supports a point load, $P,$ at the free end. Here

is a visualization of the beam's deflected shape. What is the

maximum deflection of the beam? Use the integration method.

Step $1.$ Complete the cut FBD and write M$($x$).$

Step $2.$ Write $(x).,(x)=(\frac{1}{E}I){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}M(x)dx,$ don't forget $C_1$

Step $3.$ Write $v(x).,v(x)={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(x)dx,$ don't forget $C_2$

Step $5.$ Solve $C_1$ and $C_2.$

Step $7.$ Check your answer.

Required check: Do all terms in the polynomial for $v(x)$ have units of length?

Required check: The moment diagram is linear, so that makes $v(x)$ cubic.

Do you have an $x^3$ term in your $v(x)$ equation?

yes

Required check: Tou have an $x^3$ term in your $v(x)$ equation?

Optional check: Graph your $v(x)$ function ${?}^1$ by setting $(L=10)$ and $(\frac{P}{E}I=0\mathrm{.}001).$

Does the plot look like your $v(x)$ qualitative sketch $($for $xv(x)v_{\text{m}\text{a}\text{x}}0$