1. For 0 5 ts 8, a particle moves along the x-axis so that its velocity v at time t, for given by v(t) = eD-Ei 'l. The particle is at position X = 4 at time t: 0. Part A: Write, but do not evaluate, an integral expression that gives the total distance traveled by the particle from time t= O to time t = 5. Part B: Find the position of the particle at time if: 6. Part 0: Find the average speed of the particle over the interval 0 3 ts 2. . 1 2. The function fand g are given by f(x) = x2 and gixi E): l 5. Let R be the region bounded by the xaxis and the graphs of fand g, as shown in the figure. 1 2. The function fand g are given by f(x) = x2 and 90:) 5x + 5. Let R be the region bounded by the xaxis and the graphs of fand g, as shown in the figure. (24) W) 900 -1-2-1012345678910 Part A: Find the area of R. Part B: The region R is the base of a solid. For each y, where 0 g y g 4, the cross section of the solid taken perpendicular to the yaxis is a rectangle whose base lies in R and whose height is 3y. Write, but do not evaluate an expression that gives the volume of the solid. 3. Let R be the region in the first quadrant bounded by the graph ofy = X2, the x-axis, and the line X = 3. Part A: Find the area of the region R. Part B: Find the value of h such that the vertical line x = h divides the region R into two regions of equal area. 4. Let R be the region bounded by the graph ofy = x2 and the line y = 9. Part A: Find the volume of the solid generated when R is revolved about the x-axis. Part B: There exists a number k, such that when R is revolved around the line y = k, the resulting solid has the same volume as the solid in Part A. Write, but do not solve, an equation involving an integral expression that can be used to find the value of k. 5. A graphing calculator is required for this problem. Let R and S be the regions bounded by the graphs of f(X) = sin(x) and . 1 QIXJ XT. as shown in the figure