given to correct answers without showing essential work. each of the problems to obtain partial credits. (1) (25 Points) Consider f(x) = 12 + 4x - x on the interval [0, 6]. (a) Sketch the graph of the region under the parabola y = f(x) over the interval [0, 6]; (b)Find the approximate area of the region with n = 6 (i) Use the Midpoint Rule (ii) Use the trapezoidal rule (c) Find the expression for the Riemann sum Rn, the sum of the areas of the n approximating * rectangles, by taking the regular partition and x to be the right endpoint of the kth subinterval, k = 1,2...,n; and then find the exact area of the region by taking the limit of Rn, as n & (d) Verify your result using the definite integral of f(x) over the interval [0,6]