the number of subintervals n required to approximate the integral

| August 30, 2017

Question
Problem 1: Approximate the integral
1

1

0 1 2x dx
numerically using
(a) the Trapezoidal rule with 1, 2, and 4 subintervals, i.e. by T1 , T2 and T4 , respectively.
(b) Richardson’s extrapolation R2 and R4 for the Trapezoidal rule using your answers from part (a).
(c) Simpson’s rule with 2 and 4 subintervals, i.e. by S 2 and S 4 , respectively.
(d) Richardson’s extrapolation R4 for Simpson’s rule using your answers from part (c).
(e) Gaussian quadrature I2

Problem 2: Find the number of subintervals n required to approximate the integral

1
0 1 2x dx
1

7

with an error 510

when using

(a) the Trapezoid rule Tn , and

(b) Simpson’s rule S n .

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