Derive composite Newton-Cotes rules with unequal segements (a) For the Trapozoidal rule. (h) For the Simpson's 1/3 rule. (c) The discrete data in the Table was generated using f (x)=e". Use the composite rules derived in (a) and (b) to determine the integral for these data. X, f(x,) 2.7183 3.0042 3.6693 4.9530 7.3891 9.0250 1 1.1 1.3 1.6 2.0 2.2 Table PP3 (d) Compute the true percent relative errors. 22 Recall that the true answer is [e*dx = 6.3067.

Derive composite Newton-Cotes rules with unequal segements (a) For the Trapozoidal rule. (h) For the Simpson's 1/3 rule. (c) The discrete data in the Table was generated using f (x)=e". Use the composite rules derived in (a) and (b) to determine the integral for these data. X, f(x,) 2.7183 3.0042 3.6693 4.9530 7.3891 9.0250 1 1.1 1.3 1.6 2.0 2.2 Table PP3 (d) Compute the true percent relative errors. 22 Recall that the true answer is [e*dx = 6.3067.

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

Problem PP3:
Derive composite Newton-Cotes rules with unequal segements
(a) For the Trapozoidal rule.
(b) For the Simpson's 1/3 rule.
(c) The discrete data in the Table was generated using f(x)=e".
Use the composite rules derived in (a) and (b)
to determine the integral for these data.
X,
1
1.1
1.3
1.6
2.0
2.2
f(x,) 2.7183 3.0042 3.6693 4.9530 7.3891 9.0250
Table PP3
(d) Compute the true percent relative errors.
2.2
Recall that the true answer is e*dx = 6.3067.

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