Antidifferentiation

1 05 points 3 0.5 points G(x) = -'r'+3 H(x) = -2 -7 M(x) = -x+ } J vz (5x + 3) dr = 101 + 1 + C All the three functions above are antiderivatives of the function f (x) = -2r. True True False O False 0.5 points 6 05 points 4 0.5 points 5 0.5 points Evaluate S (27 - 5x + 7) dx In evaluating fox (1 - z) de . Evaluate: S (2ex - 3) dx Evaluate: f 4 csc? (x) dx we make the substitution w = 1-2" . -15x+42 + 0 Then, for' (1 -20)'d= = ( 7 ) (1-25)' +0 O 2ex - 3 + C -4 cot? (x) + C What is the missing factor? O 2ex - + 0 O 4 cot (x) + C O O O 2ex - In |3x] + C O 4 cot? (x) + C O (23-152+42) + 0 O 2ex - 3 In|x| + C O -4 cot (x) + C o 8 1 point In evaluating ( x've + 5do . 2x dx Evaluate Jar 9 0.5 points we make the substitution w = s' +5- Evaluate: [ sin (1 - 5x) de Then ( 2' V/2 + 6ds = ( ? )(2+ 5)1+0 -2 In(1 - e27 ) + 0 What is the missing factor? - In(1 - e27 ) + 0 O cos (1 - 5x) + C O O - In(1 - ezz) + C O - cos (1 - 5x) + C O O O | sin (1 - 5z) + C O In(1 - e# ) + 0 O ; cos (1 - 5x) + C 1 point 11 05 points in evaluating J cos (z) sin' (z) dz we make the substitution u = sin (I). Consider the function g (x) = 3 + 2x on the interval [1, 4) using the Left Riemann sum with n = 6. Then. J cos (2) sin (x) da= ( ? ) sin(z)g What is the missing factor? Which of the following statements is false/incorrect? O The sum of the heights of the rectangles is 54. The width of each rectangle is ? . The given interval is [1, 4), hence, a = 1 and b = 4. The area between the graph of g and the c-axis on the interval [1, 4] is 22.5 square units. 1 point Consider the function f (z) = 2# + 2 on the interval [0. 1] using the right Reimann sum with n=4. Find the area. O 5.2187 square units O 2 4688 square units 2.2188 square units 5.2188 square units