1. Given the region R in Quadrant I bounded by: x =0, y = \\x, y=9-x (a) Sketch the region R, determine and label all intersection points, and draw one representative rectangle in the region. 107 ( b ) Determine the area of the region R by setting up and evaluating a definite integral. 1 2 3 4 5 6 7 8 9 10 2. Express the perimeter of the region R as the sum of two numbers and a definite integral ; you do not have to evaluate the definite integral.3. Compute the volume of the solid obtained by revolving the region R around the x-axis ; state whether you are using disks, shells, or washers. 4. Compute the volume of the solid obtained by revolving the region R around the y-axis ; state whether you are using disks, shells, or washers.5. Compute the volume of the solid have the region R as its base, for which vertical slices (cross-sections) parallel to the y-axis being squares. 6. Use your results in problems #1 - #4 to determine the centroid of the region R