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 ( 20.2. A new business has found that its rate of profits P (in hundreds of dollars per year) after t years of operation may be modeled by dP = 3/2 + 12+ 7. Find the profit during the 6th year of the company's operation. alllogge or Ling at 3. Find the area of the region bounded by y = 5x -, y = 0, x = 1, and x = e.4. Find the indefinite integral: COSX dx 1 + 4sinx 5. 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 y = &X. V = x - 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 OSX S .For problems 8 and 9, consider the region bounded by the two functions y = 5x-x 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.Find the arc length of the curve y = (x - 1)3/2 over the interval 16 5x $ 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.Extra Credit 1: Determine the area of the surface generated by revolving about the x-axis the are defined by y = 34/4-x for 05x54. 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 = 4