Antidifferentiation

1 0.5 points Both G (x) = 2x3 - 7x - x - 1, and H (x) = 2x3 - 7x3 - x + are antiderivatives of f (x) = 6x3 - 14x -1 True False 2 05 points 0.5 points 4 0.5 points 3 Evaluate / (x] + z) - 1) dx Evaluate: J 3dx (3241) de = 2x1 + 2x1 + C O O 2In 3x] + C True 3 In 2x] + C O =(ar'+2x]) + C O False O In|z| + C - 10 1 point * 05 points 7 8 1 point In evaluating _ 1-toss 5 0.5 points In evaluating / 12x] (5 + 27) dr . In evaluating J zv/ + 7dz . 9 0.5 points we make the substitution u = 1 - cos z . we make the substitution & = 5+ 2" we make the substitution u = z* + 7. Evaluate J d Evaluate: J -| sin (x) da = Evaluate: J sec' (3x) dr Then, [ In t dr = In( ? )+ 0 Then, / 12x) (6 + =] d - (7) (5+=]'+0 Then, [ zov/a' + 7dx = (7) (s'+ 7) +0 What is the missing argument? | cos (2) + C What is the missing factor? What is the missing factor? 12 Im(623 + 5) +0 O tan(3x) + C O cos' z + C O -1 O O In (627 +5) +0 O 3 tan(3x) + C -08 - cos (=) + C O # In(623 +5) +0 O tan(32) + C O O -1 cos (=) + C O -# In(637 +5) +c O tan (3x) + C O 1 - 005 x 11 0.5 points Consider the function g (x) = 3x - 2 on the interval [2, 6] using the Right Riemann sum with n = 6. 12 1 point Which of the following statements is false/incorrect? Consider the function / (e) = 27 + 5 on the interval |0, 1] using the midpoint Reimann sum with ned. Find the area. 5.3282 square units O The given interval is [2, 6), hence, a = 2 andb = 6. O 5.2381 square units The sum of the heights of the rectangles is 132. O The area between the graph of g and the r-axis on the interval [2, 6] is 44 square units. 5.3281 square units O The width of each rectangle is 5.2382 square units