Practice Trapezoidal Rule (4.2) - Numerical Integration - Mathematics - iii (Differential Calculus) - Vol 4

Practice: Trapezoidal Rule

Lesson 4.2Numerical Integration

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10 questions

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6 sample questions

Question 1.
What is the Trapezoidal Rule used for?
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Think about calculating areas under curves where direct integration is hard.
Question 2.
What does 'h' stand for in the Trapezoidal Rule formula?
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It's derived from the total width divided by the number of intervals.
3Question 3.
What does the Trapezoidal Rule primarily estimate?
- Area under the curve
- Rate of change
- Average value
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Consider what we are finding when we integrate.
4Question 4.
True or False: The Trapezoidal Rule gives exact results for all continuous functions.
- True
- False
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Remember the method relies on approximating regions.
Question 5.
Calculate the approximate integral of f(x) = ln(x) from 1 to 3 using the Trapezoidal Rule with n = 4. Show calculations.
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Remember to evaluate the function at the partition points and apply the trapezoidal formula.
Question 6.
Consider the function f(x) = cos(x) over the interval [0, π/2]. Apply the Trapezoidal Rule with n = 6 and analyze the convergence of the results as n increases.
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Monitor how your approximation improves with more sections!

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