AP Calculus AB 2015 Question 2 and Answers

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AP Calculus AB 2015 Free Response Question 2

2. Let f and g be the functions defined by f(x) = 1+ x + e^{x2 - 2x} and g(x) = x⁴ - 6.5x² + 6x + 2. Let R and S be the two regions enclosed by the graphs of f and g shown in the figure above.
(a) Find the sum of the areas of regions R and S.
(b) Region S is the base of a solid whose cross sections perpendicular to the x-axis are squares. Find the volume of the solid.
(c) Let h be the vertical distance between the graphs of f and g in region S. Find the rate at which h changes with respect to x when x = 1.8.

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