Consider the following curves C1 : x³ + y³ = 1 C2 : z³ + y³ = 9 C3 : y= x+1 C4 : y = 0 that are shown in the figure below. 2 R C4 2 C2 C3 -1 C1 Define the following regions, also shown in the figure above. Q is the region bounded by C3 on the left, C1 on the right, and C4 below. • R is the region enclosed by all four curves: above C, and C4, below C, and C2. (a) Use a Riemann Sum to approximate the area of the region Q. Use any rule we studied in class, andn=4 subintervals. (b) Set up integral(s) to compute the area of the region R. (c) Set up integral(s) to compute the volume of the solid obtained by rotating Q around C4.

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