Use the Composite Trapezoidal, Simpson's and Midpoint Rules to approximate the integralint_{1}^{2} x ln(x)dx, n=4(For the Midpoint Rule use n + 2 subintervals.)

aflacatn 2020-12-12 Answered

Use the Composite Trapezoidal, Simpson's and Midpoint Rules to approximate the integral
12 x ln(x)dx, n=4
(For the Midpoint Rule use n + 2 sub intervals.)

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gwibdaithq
Answered 2020-12-13 Author has 84 answers
a) Trapezoidal Rule:
The interval [1, 2 can be partitioned into 4 sub-intervals, P={1, 54, 32, 74, 2}, where:
Δ x=b  a4=14.
12 xln(x)dx=14{f(1) + 2f(54) + 2f(32) + 2f(74) + f(2)}
14{(ln(1)) + 2(54 ln(54)) + 2(32ln(32)) + 2(74ln(74)) + 2(2ln(2))}
14{0 + 0.55788589 + 1.2163953 + 1.9586553 + 2.7725887}=1.6263813
b) Simpsons
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