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Q7. Let R be the region in the first quadrant that is bounded by the curves y = er and y = 12. (a) [4 points] Sketch the region R and compute its area using an appropriate definite integral. Show all your work! (b) [2 points] Let S be a solid whose flat base is the region R and whose cross-sections perpendicular to the r-axis are squares. Find an expression for the approximate volume V(x) of a thin slice of S; this typical slice is perpendicular to the r-axis, has thickness Ar and lies between r and r + Ar. Briefly explain your answer. (c) [1 point] Give the definite integral that computes the total volume V of S. Do not evaluate the integral - just write it down