Answer: Let where is shown in the figure. Let and represent the Riemann sums using the

Chapter 0, Problem 19

(choose chapter or problem)

Let \(I=\int_{0}^{4} f(x) d x\), where f is shown in the figure. Let L(n) and R(n) represent the Riemann sums using the left-hand endpoints and right-hand endpoints of n subintervals of equal width. (Assume n is even.) Let T(n) and S(n) be the corresponding values of the Trapezoidal Rule and Simpson's Rule.

(a) For any n, list L(n), R(n), T(n), and I in increasing order.

(b) Approximate S(4).

                                               

Text Transcription:

I=int_0^4 f(x) dx