Calculus AB Assignment More Practice With Areas 1. Consider the region bounded by the curvesy = tr: + .r 12|..r = 5. and .r = 5 and the xaxis. A. Set up a sum of integrals. not containing an absolute value symbolI that can be used to nd the area of this region. E. Find the area of the region by using your answer from part A. Don't approximate with your calculator. 2. Two cars, one driven by Sappho and the other driven by Homer. start side by side at the beginning of a race; Velocities of the two cars during the race are given in the tables below where velocities is are in miles per hour and times : are in seconds. Sappho's car Homer's Car time I velocity vs time i velocity v" 0 O D D 1 20 1 18 2 35 2 31 3 4S 3 43 4 (:2 4 58 5 75 5 68 6 85 6 '3'"? 'i' 93 3" 86 S 99 8 93 9 106 9 95 10 111 10 96 Calculus AB Assignment More Practice With Areas A. Use ten trapezoids to approximate the area between the curves y = 1-50) and y = WU) on the interval from r = t} to r = 10. What denite integral are you approximating? B. If you haven't done soI convert your answer from part A into units that make good common sense for the physical situation described. Then explain what practical meaning this answer has for the physical situation. C. Estimate the average velocity of Sappho's car over the Iii-second interval using 5 subintervals and midpoints. Calculus AB Assignment More Practice With Areas 3. Consider the function f(x) = xsin(x]) on the interval [0, #/7 ], which is graphed below. 0.4 0.27 0.4 0.6 0.8 12 y = xsin(x3) A. Find a constant function (g(x) = constant) on the interval [0, 7 ] such that the area under the graph of g is the same as the area under the graph of fon the interval [0, #7 ]. (Hint: Remember that a constant function g(x) = c is just a horizontal line.) 4. Consider the curves y = x and y = mx, where m is some positive constant. No matter what positive constant m is, the two curves enclose a region in the first quadrant. Without using a calculator, find the positive constant m such that the area of the region bounded by the curves y = x and y = mx is equal to 8