6. a) Calculate midpoint Riemann sums for the function V1 + x3 on the interval (1, 3) using 40, 400, 4000, and 40000 equally-spaced subintervals. How many decimal points in this sequence have stabilized? b) Roughly how many subintervals are needed to make the midpoint Rie- mann sums for V1 + x3 on the interval (1, 3) stabilize out to the first four digits? What is the stable value? Compare this to the limiting value you found earlier for left endpoint Riemann sums. Is one value larger than the other; could they be the same? c) Comment on the relative "efficiency of midpoint Riemann sums versus left endpoint Riemann sums (at least for the function V1 + x3 on the interval [1, 3]). To get the same level of accuracy, an efficient calculation will take fewer steps than an inefficient one. 6. a) Calculate midpoint Riemann sums for the function V1 + x3 on the interval (1, 3) using 40, 400, 4000, and 40000 equally-spaced subintervals. How many decimal points in this sequence have stabilized? b) Roughly how many subintervals are needed to make the midpoint Rie- mann sums for V1 + x3 on the interval (1, 3) stabilize out to the first four digits? What is the stable value? Compare this to the limiting value you found earlier for left endpoint Riemann sums. Is one value larger than the other; could they be the same? c) Comment on the relative "efficiency of midpoint Riemann sums versus left endpoint Riemann sums (at least for the function V1 + x3 on the interval [1, 3]). To get the same level of accuracy, an efficient calculation will take fewer steps than an inefficient one