Let the region R be the area enclosed by the function f(:1:) = 6'\" + 1, the horizontal line y = 0 and the vertical lines a: = 0 and a: = 2. If the region R is the base of a solid such that each cross section perpendicular to the maxis is a rectangle whose height is half the length of its base in the region R, find the volume of the solid. You may use a calculator and round to the nearest thousandth. The shaded region shown below is bounded by the functions f(m) = 2:l:2 | 333 + 9 and g(:l:) = a: | 8 and the a\": and y axes. Find the area of the shaded region using a calculator. Round your answer to the nearest thousandth. Let the region R be the area enclosed the function f (:13) : 3em , the horizontal line y = 13, and the y-axis. Write an integral in terms of a: and also an integral in terms of :9 that would represent the area of the region R. If necessary, round limit values to the nearest thousandth. Let the region R be the area enclosed by the function f (:13) = {133, the xaxis and the vertical lines :13 = O and a\": = 2. Find the volume of the solid generated when the region R is revolved about the m-axis. You may use a calculator and round to the nearest thousandth. Let the region R be the area enclosed by the function f(:1:) = 3 1n (3:) and 9(13) = 3:13 5.Find the volume of the solid generated when the region R is revolved about the line y : 6. You may use a calculator and round to the nearest thousandth. Find the volume of the solid obtained by rotating the region bounded by $ = 3 y2 and 58 2 2y about the line a: = 9. Round to the nearest thousandth. A I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I V