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AP Calculus AB-BC 2 Pre-Final-Exam Prep Hour Name * BC Only 1. d dx [f(x)] = 2y - 4x. f(1) = 3. Use Euler's Method to approximate f(3) using 4 equal steps. 7 3 2. Let R be the region in the first quadrant bounded by the y-axis and the graphs of y = 4x - x3 + 1 and y = 4 x. 2a. Find the area of R. 4.515 2b. Find the volume of the solid generated when R is revolved about the x-axis. 18.291π 2c. R is the base of a Solid whose cross-sections perpendicular to the x-axis are semi-circles. Find the volume of this solid. 4.653 3*. 3 ⌠ ⌡x cos 2x dx = 1 3 3 2 3 3 2 x sin 2x + 4 x cos 2x - 4 x sin 2x - 8 cos 2x + C 4*. ⌠ x2 - 4x + 7 dx x3 - x2 + x + 3 ⌡ 1 2 ln x + 1 - 2 ln x2 - 2x + 3 + C | 5. | | y = f(x), f(0) = 3, | dy = x2y – x2 . Solve the differential equation for the particular solution of f(x). dx 3 y = 2e1/ 3 x + 1 6. The Velocity, v, of an object is v(t) = 6t2 - 6t + 7. The Position,s, of the object is 32 when the time, t, is 2. Find the position, s, of the object when t is 3. 62