Greetings tutor, I need your assistance with questions 6-12. Thank you!

6. Evaluate the integral. Jx(x - 3)8 dx SHOW WORK BELOW: a. x(x - 3) + ( x - 3) + c x(x -3) (x - 3) 10 9 90 +c (x - 3) 10 C. (x -3)9 10 3 + c (x - 3) 10 d. (x - 3)- 10 +c 3 e. ( x - 3 ) (x - 3) 10 9 10 -+c7. The marginal cost of producing the xth roll of film is given by 6 + - 6 (x+ 1 )2 The total cost to produce one roll is $1,000. Find the total cost function C( x ). SHOW WORK BELOW: a. C(x) = 6x + 6 x +1 + 997 b. C(x) = 6x - 6 x + 1 + c c. C(x ) = 6x + - 6 x + 1 d. C(x) = 6x - 6 * + 1 - + 997 e. C(x) = 6x - - 6 x + 18. Use the given graph to estimate the left Riemann sum for the given interval with the stated number of subdivisions. DRAW THE RECTANGLES ON THE GRAPH BELOW. [0, 3]; n =3 +2 15 25 8x -1 t-3 a. Left Sum = 1 b. Left Sum = 2 C. Left Sum = - 2 d. Left Sum = 0 . Left Sum = - 1 9. Calculate the left Riemann sums for the function over the given interval, using the given values of n. (When rounding, round answers to four decimal places.) Use your calculator for this problem. No work is required. f ( x) =- X over [0,2], n = 5 a. Left sum = 0.3548 b. Left sum = 1.7738 C. Left sum = 8.8688 . Left sum = 0.7095 e. Left sum = 1.419010. The graph of the derivative f (t) of f() is shown. Compute the total change of f(t) over the interval [2,8]. f 'it) 2.5 2 1.5 1 -0.5 SHOW WORK COMPUTING THE TOTAL CHANGE BELOW: a. f(8) -f(2) = 60 b. f(8) - f(2) = 24 c. f(8) -f(2) = 15 d. f(8) -f(2) = 9 e. f(8) - f(2) = 3011. The rate of change r(r} of the total number, in thousand of articles, of research articles in the prominent journal Physics Review written by researchers in Europe is shown in the graph, where t is time in years {I = 0 represents the start of 1987). Use both left and right Riemann sums (take the average of the two values as your estimate) with 7 subdivisions to estimate the total number of articles in Physics Review written by researchers in Europe in the 14-year period beginning 1981 {Estimate each value of r{t) to the nearest 0.5). Use the sums 14 to obtain an estimate of Ill-(r) d2. 0 SHOW WORK TO THE RIGHT OF THE GRAPH. a. 8,000 articles b. 56,000 articles c. 52,000 articles 11. 4,000 articles e. 60,000 articles 12. Calculate the total area of the region bounded by the line y = 20x, the x-axis, and the lines x = 8 and x = 18. SHOW WORK BELOW: 5,200 53,200 2,600 d. 200 100