HW # 2 Integrals and more 1) Calculate the following indefinite integrals a) S(x4+ 3x - 8) dx b ) S (3ex + 2cosx) dx c) S (tanx) dx 2) Evaluate the following definite integrals a) So (x2 + 1) dx 10 e10ox 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, 7] 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 + y2 - z