The table shows values of a force function f(x), where x is measured in meters and f(x) in newtons. Use the Midpoint Rule with n = 4 to estimate the work W done by the force in moving an object from x = 5 to x = 21.W = Jx 5 7 9 11 13 15 17 19 21f(x) 5 5.6 6.8 8.8 9.4 8.2 6.9 5 3.9

The Midpoint Rule is a numerical method used to approximate the definite integral of a function. In this case, we are using it to estimate the work done by a force, which is the integral of the force over the distance moved.

The Midpoint Rule states that the integral of a function f from a to b is approximately equal to (b - a) * f((a + b) / 2), where (a + b) / 2 is the midpoint of the interval [a, b].

Given that n = 4, we divide the interval from x = 5 to x = 21 into 4 subintervals. These subintervals are [5, 9], [9, 13], [13, 17], and [17, 21].

We then find the midpoint of each subinterval and evaluate the force function f at these midpoints. The midpoints are 7, 11, 15, and 19. The corresponding force values are 5.6 N, 8.8 N, 8.2 N, and 5 N.

We then multiply each force value by the length of the subinterval (which is 4 m in each case) to get the work done over each subinterval. This gives us 22.4 J, 35.2 J, 32.8 J, and 20 J.

Finally, we add up these values to get the total work done, which is 22.4 J + 35.2 J + 32.8 J + 20 J = 110.4 J. So, the work done by the force in moving the object from x = 5 to x = 21 is approximately 110.4 J.