1. (8 points) Find f(x) if f'(x) = 3x2 + 2 and f(1) = 4 2. (8 points) Find f'(x) if f(x) = (x2 + 1)in(24 + 6). 3. (10 points) Use a Riemann sum to approximate S, Thadx. Let the number of subin- tervals ben = 4 and use the midpoints of the subintervals as the selected points in the sum. 4. (16 points) Find the area of the region bounded by the curvesy = x2 + x + 2 and y = 5- x. 5. (14 points) A certain cell culture grows at a rate proportional to its size. In 4 hours a population of 40,000 grew to 160,000. How large will the population be after 12 hours ? 6. (14 points) Find the volume of the solid of revolution generated by revolving about the x-axis the region bounded by the curvey = e- and the x-axis from x = 0 to x =1. 7. (30 points) Find (a) Sadx e (In(x))2 dx ( b ) s (c) [Axe dx