HW # 2 Integrals and more 1) Calculate the following indefinite integrals a) J(x* + 3x - 8)dx b) S (3e* + 2cosx)dx c) J (tanx) dx 2) Evaluate the following definite integrals XP ( I + z x ) fle 10 e 10ox b) 10 In (x2 +1) -dx c) S, Inx 3) Calculate the mean value of the function f (x) = 2 sinx on the interval [0, x] 4) Determine the area of the region bounded by the graphics of the functions f(x) = 3 and g(x) = x between the points x = 0 and x = 3. 5) Construct the differential and the gradient of the function f (x, y, z) = x2 + y? - z