Apply the Midpoint and Traperold Rules to the following integral Make a table showing the approximations and errors for 48, 16, and 32. The exact value of the ntegral g for computing the enointegrate Ex * e ^ (- 2x) dx from 0 to 1/2 = 3(1 - e ^ - 5) = 2.9f(t) * 6Complete the following tableCrpe brogers or decimals Round to four decimals places as needed)T(-)Absolute Error in Mn)Absolute Error in T(x)

Integration over discontinuities. Integrate the function f(x) = 0 for x < 1, f(x) = exp(x − 1) + exp(2 − x) for 1 ≤ x ≤ 2, f(x) = 0 for x > 2 from x = 0 to x = 3, for varying step sizes, using the trapezoidal method. Plot the error as a function of step size. A Matlab function calculating this function, f_r13a.m, is available on Blackboard. Note that the integral is equal to 2e − 1. use matlab and show me the codes

EXAMPLE 5 Use the Midpoint Rule with n = 5 to approximate the following integral.43x dx2SOLUTION The endpoints of the subintervals are 2, 2.4, 2.8, 3.2, 3.6, and 4, so the midpoints are 2.2, 2.6, 3, 3.4, and . The width of the subintervals is Δx = (4 − 2)/5 = , so the Midpoint Rule gives43x dx2≈ Δx[f(2.2) + f(2.6) + f(3) + f(3.4) + f(3.8)] =  0.432.2 + 32.6 + 33 + 33.4 + 33.8≈ . (Round your answer to four decimal places.)Since f(x) = 3x > 0 for 2 ≤ x ≤ 4, the integral represents an area, and the approximation given by the Midpoint Rule is the sum of the areas of the rectangles shown in the figure.

Integration over an infinite interval. Integrate exp(−x) from x = 0 to x = ∞, by numerically integrating from x = 0 to increasing values of x. Plot a graph of the error vs the value of x you integrate to. Compare results for a fixed step size and a fixed number of steps. use matlab to finish show me the codes

Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places. 880sin(x) dx,    n = 4

Let f (x) = x2 −1 and I = [1, 4]. Find the right-hand side approximation R3 to S41f (x)dx.Recall that Rn is the right-endpoint approximation using n rectangles of equal width.A. 12B. 11C. 17.75D. 26E. 23