Practice Simpson’s 1/3 Rule (4.3) - Numerical Integration - Mathematics - iii (Differential Calculus)

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6 sample questions

Question 1.
What must n be in Simpson's 1/3 Rule?
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Think about the number of intervals needed.
Question 2.
What does h represent in the formula?
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How do you find the width of each segment?
3Question 3.
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.
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Think about how shapes differ in fitting a curve.
4Question 4.
True or False: Simpson’s 1/3 Rule requires an odd number of intervals.
- True
- False
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Consider what makes it effective.
Question 5.
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.
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Make sure to correctly identify your function evaluations at each breakpoint.
Question 6.
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?
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Recap how the fourth derivative impacts the estimation of error.

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