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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the order of accuracy for the Trapezoidal Rule?
💡 Hint: Think about how the approximation improves when you increase the number of intervals.
Question 2
Easy
Can the Trapezoidal Rule be used with any number of intervals?
💡 Hint: Recall the conditions for the different rules.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the order of accuracy for Simpson's 1/3 Rule?
- O(h)
- O(h²)
- O(h⁴)
💡 Hint: Consider how the order relates to precision in integration.
Question 2
True or False: The Trapezoidal Rule requires the number of subintervals to be even.
- True
- False
💡 Hint: Recall the specific rules associated with each method.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a smooth curve y = x³ over the interval [0, 1], derive both the Trapezoidal Rule and Simpson's 1/3 Rule estimates for n = 4.
💡 Hint: Make sure to calculate the average of the endpoints for Trapezoidal.
Question 2
If a function is oscillating and you want better accuracy using Simpson’s 3/8 Rule, what should you consider about your number of intervals?
💡 Hint: Look at how you set your data points in practice.
Challenge and get performance evaluation