Question 1. Consider the function f(x) = xcos(x) in the interval [0, 27]. Within the interval (0, 27), the critical points of f(x) are at x = 0.86 and x = 3.426. Also, the critical points of f'(x) are at x = 2.289 and x = 5.087. (a) [1 point] Sketch the graph of f(x) in the interval [0, 27]. Shadow the region bounded by the curve y = f(x) and the x-axis. (b) [2 points] Use the Fundamental Theorem of Calculus II to find the area of the shaded region in Part (a), i.e., .2 TT (x cos(x ) |da. (c) [1 point] Rotate the shaded region described in Part (a) around the x-axis to generate a solid. A cross-sectional region A(x) at a point x on the x-axis (the axis of rotation) is obtained by intersecting the solid with a plane perpendicular to the x-axis passing through x. Describe the shape of A(x) and determine the area of A( T). (d) [2 point] Evaluate (e) [1 point] Divide the interval [0, 27] into n equal subintervals [xi-1, x;]. Consider the following limit of the sum of the volumes of disks with radius |2ni cos(2mi ) | and thickness 27, 2 TT V = lim COS i= 1 n n nConsidering Part (d), is the following true? A(x) dx = V. Justify your answer. (f) [1 point] Find the volume of the solid