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I have the solution's manual for this particular problem, but I'm having hard time understanding the steps they've taken. I've attached pictures of the problem below.

For the shear, are they using 1/2*x*(wx/L) because it is equal to the area of the force?

And for the bending moment, where are they getting x/3 from? is that the from the centroid's distance?

For the shear, are they using 1/2*x*(wx/L) because it is equal to the area of the force?

And for the bending moment, where are they getting x/3 from? is that the from the centroid's distance?

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