Complete the problems below using direct integration of load to find equations for shear and moment and to plot the shear and moment diagrams. In doing so$,$ ensure you:

$$ Find equations for load, shear, and moment for all regions of the beam

$$ Identify all discontinuities in the beam and corresponding regions of analysis

$$ Use the direct integration of load method $($other methods will be marked as incorrect$)$

$$ Correctly identify boundary conditions and clearly show how they are applied to the problem in each region

$$ Draw your shear and moment diagrams below a diagram of the beam using the format we use in class

$$ Write equations of shear and moment directly on the diagrams

$$ Identify values of shear and moment at each discontinuity

$$ Identify locations of maximum$/$minimum moment that may occur between discontinuities and provide the values directly on the diagrams