Although a calculator is permitted, ALL WORK must be shown.

Please provide detailed answers to the questions listed below.

This Question is **CALCULATOR ACTIVE** Let R be the region in the first quadrant bounded by the X-axis and the graphs of y = 4 -x and y = ln(x 1), as shown in the figure below. (a) Find the area of R. (b) Region R is the base of a solid. For the solid, each cross section perpendicular to the y-axis is a square. Write, but do not evaluate, an expression involving one or more integrals that gives the volume of the solid. (0) The horizontal line )2 = 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