Practice Comparison of Rules - 4.5 | 4. Numerical Integration | Mathematics - iii (Differential Calculus) - Vol 4
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Comparison of Rules

4.5 - Comparison of Rules

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Learning

Practice Questions

Test your understanding with targeted questions

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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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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