2. The function f and g are given by f(x) = x2 and g(x)= --x+5. Let R be 2 the region bounded by the x-axis and the graphs of f and g, as shown in the figure. 6 5 (2,4) 4 3 f(x ) g(x) R X -2 -1 0 1 2 3 4 5 6 7 8 9 10Part A: Find the area of R. Part B: The region R is the base of a solid. For each y, where {J E y a 4, the cross section of the solid taken perpendicular to the vaxis is a rectangle whose base lies in R and whose height is 3y. Write, but do not evaluate an expression that gives the volume of the solid. Part C: Write an expression that can be used to calculate the total length of the curve on the domain [0, 10] and nd the length. Part D: Rewrite the curve x] = x2 in terms of y and write the denite integral that can be used to determine the length of the curve fly). 3. Let R be the region in the rst quadrant bounded by the graph of y = x2, the xaxis. and the line x = 3. Part A: Find the area of the region R. Part E: Find the value of it such that the vertical line x = h divides the region R into two regions of equal area. 4. Let R be the region bounded by the graph of y = x2 and the line y = 9. Part A: Find the volume of the solid generated when R is revolved about the xaxis. Part B: There exists a number k, k s O. such that when R is revolved around the line v = k, the resulting solid has the same volume as the solid in Part A. Write, but do not solve, an equation involving an integral expression that can be used to nd the value of k. Let R and S be the regions bounded by the graphs of f(x) = sin(x) and g(x) = = x -1 5 as shown in the figure. A 3 2 S 0 R -1 -2 -3 45 -4 -3 -2 -1 0 1 2 3 4 5 Part A: Find the area of R + S. Part B: The region R is the base of a solid. For this solid, each cross- section perpendicular to the x-axis is a semicircle. Find the volume of this solid. Part C: Write the definite integral that is used to determine the length of the curve f(x) that bounds the regions R and S, and then evaluate it