Calculus AB Assignment More Applications of Integrals 1. Consider the curve 3' =x) = 21' l. A. Find the exact area of the region in the rst quadrant bounded by the curves y =x) = 2x 1 and y = x. ("Exact area" means no calculator numbers.) E. Find the inverse function y =f1(x). C. Using part A and the notion of symmetry between a function and its inverse, find the exact area of the region in the first quadrant bounded by the curves 5* =f'1(x) and y = x. Explain your reasoning. (Hint: Think "graphically" and little or no math will need to be done!) D. Find a value for a such that the average value of the function fix) on the interval [0m] is equal to 1. You may use a calculator here. Calculus AB Assignment More Applications of Integrals 2. A particle moves on a coordinate line with an acceleration at time : seconds of el/2 m/sec2. At 1= 0 the particle is at the origin, and its velocity is -4 m/sec. A. Find a function v() that gives the velocity of the particle at time t. B. At what (exact) time is the velocity of the particle 0 m/s? C. Set up an expression (which may contain integrals, but not absolute values) to find the total distance traveled by the particle from time : = 0 to t = 6. You do not have to solve your expression. 3. A culture of bacteria is growing at a rate of 4e0-5 per hour, with : in hours and 0 s t s 20. A. How many new bacteria will be in the culture after the first six hours?Calculus AB Assignment More Applications of Integrals B. How many new bacteria are introduced from the end of the fifth hour through the fifteenth hour? C. At approximately how many hours after r = 0 will the culture contain 200 new bacteria? 3 4. Consider the functionsx) = i 1 and g(x) = f . Let R denote the region in the first I + x +1 quadrant bounded by the curves y =x] and y = g(x). Find the exact volume of the solid that has R as its base if every cross section by a plane perpendicular to the xaxis is a rectangle of height 3. ("Exact volume" means no calculator numbers.)