Let R be the region in the first quadrant bounded by the x-axis and the graphs of y =ln x and y=5−x.
A) Find the area of R.
B) Region R is the base of a solid. For the solid, each cross section perpendicular to the x-axis is a square. Write, but do not evaluate, an expression involving one or more integrals that gives the volume of the solid.
C) The horizontal line y=k divides R into two regions of equal area. Write, but do not solve, an equation involving one or more integrals whose solution gives the value of k.