1. An object has an acceleration function of a() = 10cos4t ft./sec. , an initial velocity vo = 5 ft./sec., and an initial position xo - - 6 ft. Find the specific position function x(t) which describes the motion of this object along the x-axis for ( 20.3. Find the area of the region bounded by y = 5x 2- , y =0, x = 1, and x = e.Extra Credit 2: Find the volume of the solid generated by revolving about the y-axis the region bounded by the graphs of x = 2tan x = 0 and y 4Extra Credit 1: Determine the area of the surface generated by revolving about the x-axis the arc defined by y = 34/4-x for 05x54.2. A new business has found that its rate of profits P (in hundreds of dollars per year) after ? years of operation may be modeled by dr = 3/2+ 12r+7. Find the profit during the 6th year of the company's operation.\f5. Find the area of the region in the first quadrant that is bounded by the curves y = ex and y = ex and the line x = In4.6. Find the area of the region bounded by the graphs of the equations V - 8x, y= r = 1 and the x-axis.7. Find the volume of the solid generated by revolving about the y-axis the region bounded by the graph of the function y = 3sin(x2) and the x-axis for OSXS n.For problems 8 and 9, consider the region bounded by the two functions y = 5x-x2 and y= X. 8. Find the area of this region in the x-y plane.9. Find the volume of the solid generated by revolving the specified region about the line x = 4.10. Chose one of the following two problems. The alternate may be counted as extra credit, If both problems on this page are worked, mark the one to be counted as extra credit. Find the arc length of the curve y = WIN (x - 1)3/2 over the interval 16 S x S 25.A cable which weights 8 1b./ft. (by itself) has a 1000 lb. object attached to its end. If the object is hanging 350 ft. below the surface in a mine shaft, find the amount of work needed to pull the cable and the object up to ground level