(1) Evaluate or determine the definite integral: a) 2n | sintldt, b) ST Edt, c) She tat. (2) Find the area of the region bounded by the parabolas: y = x2 and y = (x -1)2 + 1. Include a sketch in your solution. (3) Find the volume of the solid obtained by rotating the triangle (2, 0) (2, 4) (1, 1) about the horizontal axis. (4) Find the volume of the solid obtained by rotating the triangle (2, 0) (2, 4) (1, 1) about the vertical axis. (5) Graph f(t) = tsin . Find the average value of of t sin ~ over [0, 1]. Then evaluate the limit of this average as N - o.. (6) Calculate the arc length of y = In (cos x), 0