4.5 - Comparison of Rules
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Practice Questions
Test your understanding with targeted questions
What is the order of accuracy for the Trapezoidal Rule?
💡 Hint: Think about how the approximation improves when you increase the number of intervals.
Can the Trapezoidal Rule be used with any number of intervals?
💡 Hint: Recall the conditions for the different rules.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the order of accuracy for Simpson's 1/3 Rule?
💡 Hint: Consider how the order relates to precision in integration.
True or False: The Trapezoidal Rule requires the number of subintervals to be even.
💡 Hint: Recall the specific rules associated with each method.
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Challenge Problems
Push your limits with advanced challenges
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.
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.
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