. Use integrals to nd the area of the triangle with vertices (1, 1), (3, 5), and (6, 1). . Find the area of the region bounded by y = cos(a:) and y = sin(:r:) from :1: = 0 to 2: = 7r / 3. . Let m and n be positive whole numbers such that n > m > 0. Find the area of the region in the rst quadrant bounded by y 2 arm and y = m" (a) using an integral with reSpect to :13. (b) using an integral with respect to y. (c) Show that your answer in (b) is equal to your answer in (a). . The average value of a function equals 4 for 1 S a: S 6, and equals 5 for 6 S a: g 8. What is the average value of the function for 1 g :1: S 8? . Find the number(s), b, such that the average value of f (as) = 2 + 6:1: 3:132 on the interval [0, b] is equal to 3. . The velocity of a particle, in centimeters per second, is given by t2 1035 + 24. Find the total distance traveled by the particle over the interval 0 S t g 10. t3 31:2 . The position of a car, in km, at time t hours is given by ? + ? 215. (a) Find the displacement of the car after 5 hours. (b) Find the total distance traveled by the car after 5 hours