The velocity of an object moving along a line is given by v = 2t + 1 ft/s on the interval 1 st$ 5. a. Divide the interval [1, 5] into subintervals, [1, 2], [2, 3], [3, 4], and [4, 5]. On each subinterval, assume the object moves at a constant velocity equal to the value of v evaluated at the midpoint of the subinterval and use these approximations to estimate the displacement of the object on [1, 5]. (See part (a) of the figure.) b. Repeat part (a) for n = 8 subintervals (see part (b) of the figure). Click the icon to view the figures. - . . a. For n = 4 subintervals, the approximate displacement of the object is |ft. (Simplify your answer.) b. For n = 8 subintervals, the approximate displacement of the object is |ft. (Simplify your answer.)Complete the following steps for the given function, interval, and value of n. a. Sketch the graph of the function on the given interval. b. Calculate Ax and the grid points X, X1 , ..-; Xn. c. Illustrate the left and right Riemann sums, and determine which Riemann sum underestimates and which sum overestimates the area under the curve. d. Calculate the left and right Riemann sums. f(x) = cos (x - 1/2) on [3x/8,7x/8]; n=4 a. Sketch the graph of f(x) = cos (x - 1/2) on the interval 8 8 Choose the correct graph below. O A. O B. O c. OD. 2- X of b. Ax= (Type an exact answer, using it as needed.) List the grid points. (Use a comma to separate answers as needed. Type exact answers, using it as needed.) c. Illustrate the left Riemann sum. Choose the correct graph below. O A. O B. O C. O D.c. Illustrate the left Riemann sum. Choose the correct graph below. O A. O B. O C. OD. 2- N 1- Ay 1- 0.5- 0.5- X X it X 1/2 Illustrate the right Riemann sum. Choose the correct graph below. O A. O B. O C. O D. 1- 1- 2- 0.5- 0.5- X X X 1/2Which Riemann sum underestimates and which sum overestimates the area under the curve? O A. The left Riemann sum underestimates the area and the right Riemann sum overestimates the area. O B. Both sums underestimate the area O C. The right Riemann sum underestimates the area and the left Riemann sum overestimates the area. O D. Both sums overestimate the area. d. The left Riemann sum is . (Round to two decimal places as needed.) The right Riemann sum is . (Round to two decimal places as needed.)Complete the following steps for the given function, interval, and value of n. a. Sketch the graph of the function on the given interval. b. Calculate Ax and the grid points x0. x1, X\". c. Illustrate the midpoint Riemann sum by sketching the appropriate rectangles. d. Calculate the midpoint Riemann sum. 2 f(x)=+1on[2,7];n=5 2 a. Sketch the graph of f(x) = E +1 on the interval [2,7]. Choose the correct graph below. b. Ax: _is the grid points. {Use a comma to separate answers as needed. Simplify your answers.) c. Illustrate the midpoint Riemann sum. Choose the correct graph below. O A. O B. Ay O C. 2.5- 2.5- Ay 2.5- 1.25- 1.25- 1.25- X X CO- CO- d. The midpoint Riemann sum is . (Round to two decimal places as needed.)