be organized i need every single problem sloved in wrritten in paper clear with step by step and show the work please

Due date: 11/06/2023 (11:59 PM) Problem 6 Problem 1. Evaluate 2x2(2 - x)2 dx. Provide a rough check of your answer by sketching the graph of the graph of Find the following integrals by using formula of a power function (choose 4 integrals to solve). the integrand f(x) = 2x2(2 - x)2 over the interval [0, 2]. x dr (b ) xvidx (c) dx Problem 7 (a) (e ) ex dx ( 8 ) 3e-2x dx (h) / 2' dx Compute the areas under the graphs, over [0, 1], of: (a) f(x) = x3; (b) f (x ) = x10. Problem 2 Problem 8 Find the following integrals by using formula of a power function (choose 4 integrals to solve). Compute the area bounded by the graph of each of the following functions over the indicated (a ) ( 13 + 2x - 3 ) dx (b) (x - 1)2 dx (c) ( x - 1) ( x + 2) dx interval. In (c), sketch the graph and indicate by shading the area in question (solve c) and any other function of the remaining) (d ) (x + 2 ) 3 dx ( e ) ( 3x - @ 2 + ex ) do ( f ) x -3x+ 4 - dx x (a) f(x) = 3x2, in [0, 2] (b) f(x) = x, in [0, 1] Problem 3 (c) f(x) = el, in [-1, 1] (d) f(x) = 1/x2, in [1, 10] (a) If f'(x) = -3x2 + 2x- 1 and f(1) = 3, what is f(x)? Problem 9 (b) If marginal cost is C'(x) = x2 + x + 200, and fixed cost is C(0) = 2000, what is C(x)? Compute the area bounded by the graph of f(x) = 1/x3, the x-axis, and the two lines x = -2 and (c) Assume that the marginal cost function of a firm is C'(x) = 2x2 + 5x + 100 and that the fixed costs are 50. Find the cost function. x = -1. Make a drawing. (Hint: f(x)