Purchase Solution

Composite Trapezoidal Rule, Simpson's Rule and Gaussian Quadratures

Not what you're looking for?

Ask Custom Question

1. Use the composite Trapezoidal Rule with indicated values of n=4 to approximate the following integrals

See Attached file for integrals.

2. Use the Excel programs for Simpson's composite rule to evaluate integrals in Problem 1.

3. Use Gaussian Quadratures with n = 2, n = 4, n = 5 to evaluate integrals in Problem 1.

4. Find exact values of the integrals given in Problem 1. Compare errors in approximate values of the integrals.

5. Give a comparative analysis of errors made by the Trapezoidal Rule, and Simpson rule. Explain for what kind of functions The Simson's rule gives an exact result for the integral. Explain why.

6. For the improper integral of the following type , (See attached File) please explain in what case it is convergent, and in what case its divergent. Bring an example. Also explain for what value of p we can apply the Simpson's rule?

Purchase this Solution

Solution Summary

Integrals are calculated using the composite trapezoidal rule, Simpson's rule and Gaussian quadratures. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

Purchase this Solution

Free BrainMass Quizzes
Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Probability Quiz

Some questions on probability