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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What must n be in Simpson's 1/3 Rule?
💡 Hint: Think about the number of intervals needed.
Question 2
Easy
What does h represent in the formula?
💡 Hint: How do you find the width of each segment?
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 key advantage of using Simpson's 1/3 Rule compared to the Trapezoidal Rule?
- It's simpler to compute.
- It provides higher accuracy.
- It's always faster.
💡 Hint: Think about how shapes differ in fitting a curve.
Question 2
True or False: Simpson’s 1/3 Rule requires an odd number of intervals.
- True
- False
💡 Hint: Consider what makes it effective.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Estimate the integral of f(x) = e^x from 0 to 1 using Simpson’s 1/3 Rule with 4 intervals. Provide a complete solution.
💡 Hint: Make sure to correctly identify your function evaluations at each breakpoint.
Question 2
Evaluate the error for f(x) = cos(x) over [0, π/2] using Simpson's 1/3 Rule. What does it tell you about the accuracy?
💡 Hint: Recap how the fourth derivative impacts the estimation of error.
Challenge and get performance evaluation