$8-6.$ Determine the maximum deflection between the supports $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash ).$ EI is constant. Use the method of integration.

Use of the double integration method $($or called the method of integration as we cited in class$)$ to determine slope and deflection functions. Then determine the maximum deflection between $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash ).$

If you can plot the resulting slope and deflection curves $+5$ pts $.$

Note that for this problem, the picture above only hints that a cut section between C and A$.$ It needs another cut between $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$ to define the moment function. The variable for the first cut is x$1,$ for the second cut, you can use x$2$ starting from $\backslash ($ A $\backslash )$; or start from $\backslash ($ C $\backslash )$ directly, in this case, just use one $\text{'}\backslash ($ x $\backslash )\text{'}.$

Be aware of the boundary condition at A$.$ How many useful BC$\text{'}$s there?

Another note: when you determine the moment function, you can choose to use the method of integration too instead of the basic method $($NOTE: the loading function $\backslash ($ w$($x$)=-$w$!!!)\backslash )$; and then use the FBDs for C$-$B and A$-$B to determine the force boundary conditions to solve for the constants. This integration method conforms to the ordinates you choose $($e$.$g$.$ either two $\backslash ($ x $\backslash )$ or one $\backslash ($ x$)\backslash ).$