Consider the following table of data:0.20.40.60.81.01.21.4f (x)131118274056a) Use second order accurate O(h?) forward, backward and centered divided differenceequations to determine the second derivative of f(x) at x = 0.8.b) Compute the integral of the function using the trapezoidal rule, Simpson's 1/3 rule, andSimpson's 3/8 rule in the interval of [0.2 – 1.4].

We'll answer one question, since the exact one wasn't specified. Please re submit the question which…

Answered: b) Compute the integral of the function…

b) Compute the integral of the function using the trapezoidal rule, Simpson's 1/3 rule, and Simpson's 3/8 rule in the interval of [0.2 – 1.4].

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.

Question

Consider the following table of data:
0.2
0.4
0.6
0.8
1.0
1.2
1.4
f (x)
1
3
11
18
27
40
56
a) Use second order accurate O(h?) forward, backward and centered divided difference
equations to determine the second derivative of f(x) at x = 0.8.
b) Compute the integral of the function using the trapezoidal rule, Simpson's 1/3 rule, and
Simpson's 3/8 rule in the interval of [0.2 – 1.4].

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