AB Module 8 DBA: This is a non-calculator assignment. Please show all your work to support your answers. The graph of f(x) = 8-x³ and the line / which is tangent to f at x = 1 is shown in the figure below. The equation for line / is y=-3x + 10. Region R is the shaded region between line I, the graph of f and the y-axis while S is the shaded region between line I, the graph of f and the x-axis. y R (1,7) y=8-x' line / S (a) Find the area of the shaded region R. (b) Region R is the base of a solid. For this solid, each cross-section perpendicular to the x-axis is a semi-circle. Write, but do not evaluate, an integral expression that would compute the volume of the solid. (c) Region S is rotated about the y-axis. Write, but do not evaluate, an integral expression that would compute the volume of the solid. (d) In quadrant 1, the region formed by x-axis, y-axis and f(x) is rotated about the x-axis. Write, but do not evaluate, an integral expression that would compute the volume of the solid.

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