The symbols T n and S n are defined as the estimates of the integral using n

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The symbols Tn and Sn are defined as the estimates of the integral

Df=1 I (1 + 2x) dx

using n intervals with the trapezium and Simpson’s rules respectively. Calculate T1, T2, T4, S2 and S4, working to 3dp only. Verify that your numerical results satisfy

S2n = (4Tn - T,)

for n = 1 and 2. Prove this result.

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