In this problem we will evaluate the following definite integral using Riemann sums: (4-5x) dx (a)...

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In this problem we will evaluate the following definite integral using Riemann sums: (4-5x) dx (a) Suppose we approximate this integral with an n-term Riemann sum, using subintervals of equal width and right endpoints in an expression of the form R = [f(xi) Ax. i=1 Find Ax, xi, and f(x;). (Your answers may depend on n and/or i.) Ax: = Xi = f(x) =_ (b) Express the quantity R in part (a) in terms of n only, with no "E" remaining. These standard formulas may help: n Rn = i=n(n+1) 2 " So (4-5x) dx: = ; lim R = n0 = (c) Finally, apply the limit as n to evaluate the given in- tegral: n(n+1)(2n+1) 6 In this problem we will evaluate the following definite integral using Riemann sums: (4-5x) dx (a) Suppose we approximate this integral with an n-term Riemann sum, using subintervals of equal width and right endpoints in an expression of the form R = [f(xi) Ax. i=1 Find Ax, xi, and f(x;). (Your answers may depend on n and/or i.) Ax: = Xi = f(x) =_ (b) Express the quantity R in part (a) in terms of n only, with no "E" remaining. These standard formulas may help: n Rn = i=n(n+1) 2 " So (4-5x) dx: = ; lim R = n0 = (c) Finally, apply the limit as n to evaluate the given in- tegral: n(n+1)(2n+1) 6