AP Calc 8.4 Review Stations

Station 1: [Calculator active] Let)' and g be the functions given byfljx) = ex and g(x) = In 37. Find the area of the region enclosed by the graphs offand 5: between 1: = i and x = 1. Station 2: [NO CALCULATOR] . 9 . . . . . . The expresSIon f0 (12 - dNada: gives the area of a region R In the first quadrant. Write an equwalent expression using horizontal rectangles. Station 3: [N0 CALCULATOR] Let R be the region in the first quadrant enclosed by the graphs off(x) = 8x3 and 90:) = sin(ri:x). Find the area of region R. Station 4: [Calculator Active} Let R be the region in the first quadrant enclosed by the graphs of f(x} = lnx and g(x) = S x. The horizontal line 3.? = k divides region 1'? into two equal areas. Write, but do not solve, an equation involving integrals, whose solution gives the value of k. -.|' 0 I Station 5: [N0 CALCULATOR] Let R be the region bounded by the yaxis, the vertical line at = 2, the horizontal line 3) = 6, and the graph of y = 4- ln(3 - x) as shown in the figure below. a] Write, but do not solve, an integral expression that gives the area ' of region R using vertical rectangles. b} Write, but do not solve, an integral expression that gives the area of region R using horizontal rectangles. Station 6: (NO CALCULATOR) (Multiple Choice) Which of the following integrals correctly gives the area of the region above the x-axis but below the curve y = 14 - 5x - x2? A) , (14 - 5x - x2) dx B) ,(x2 + 5x - 14) dx C) ( x2 + 5x - 14) dx D) 2 (14 - 5x - x2) dx E) , (14 -5x - x2) dx Station 7: (Calculator active) a) Write, but do not solve, an integral that will compute the area of the region bounded by x2 + y' = 4 between x = -t and x = t whenever-2 s t s 2. b) Evaluate the integral for t = 2. Station 8: (Calculator Active) Let R be the region bounded by y = sin(x) and y = x3 - 4x as shown on the right. a) Find the area of region R. -2 -3- b) The horizontal line y = -2 splits R into two regions. Write, but do not solve, an integral expression that would give the area of the part of R that is below this horizontal line