Practice Gaussian Quadrature Example (3.4.3) - Numerical Differentiation and Integration

Practice: Gaussian Quadrature Example

Lesson 3.4.3Numerical Differentiation and Integration

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9 questions

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6 sample questions

Question 1.
What does Gaussian quadrature aim to improve?
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Think about how it selects points in the integration process.
Question 2.
What are the nodes used in the Gaussian quadrature example?
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Recall the specific points from our example.
3Question 3.
What is the primary goal of Gaussian quadrature?
- To simplify integrals
- To maximize accuracy with few nodes
- To increase computational time
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Consider how it relates to reducing error.
4Question 4.
True or False: Gaussian quadrature requires a larger number of points to achieve high accuracy.
- True
- False
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Think about the efficiency of the method.
Question 5.
Consider the integral \int_{0}^{2} x^2 e^{-x} , dx. Set up a 2-point Gaussian quadrature approximation for this integral and determine the approximate value.
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Identify your function and then apply the Gaussian quadrature formula.
Question 6.
Suppose we use 4-point Gaussian quadrature for the integral \int_{-1}^{1} , sin(x) , dx. Calculate the integral approximation and compare it to its exact value.
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Refer to the standard nodes and weights for a 4-point Gaussian quadrature.

5 more questions in this section. Enroll free to practise them all.