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Questions and Answers
When evaluating a definite integral as the limit of a sum, what does 'f(x)' represent?
If an interval [a, b] is divided into 'n' equal parts of width 'h', what does 'h' represent?
In the context of evaluating definite integrals as limits of sums, what does 'n' represent?
What is being evaluated when considering definite integral as the limit of a sum?
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What happens to the accuracy of the evaluation as the number of subdivisions 'n' increases?
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In the context of evaluating definite integrals as limits of sums, what does 'h' represent?
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What does 'n' represent when an interval [a, b] is divided into 'n' equal parts of width 'h'?
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When evaluating definite integrals as limits of sums, what is the significance of increasing the number of subdivisions 'n'?
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What is being evaluated when considering definite integral as the limit of a sum?
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In the context of evaluating definite integrals as limits of sums, what does 'f(x)' represent?
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In the context of evaluating definite integrals as limits of sums, what does 'h' represent?
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What is the significance of increasing the number of subdivisions 'n' when evaluating a definite integral as the limit of a sum?
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What does 'n' represent when an interval [a, b] is divided into 'n' equal parts of width 'h'?
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When considering definite integral as the limit of a sum, what does 'f(x)' represent?
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What happens to the accuracy of the evaluation as the number of subdivisions 'n' increases?
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Study Notes
Evaluating Definite Integrals as Limits of Sums
- 'f(x)' represents the function being integrated.
- When an interval [a, b] is divided into 'n' equal parts, 'h' represents the width of each part, given by (b-a)/n.
- 'n' represents the number of equal parts or subdivisions of the interval [a, b].
- When evaluating a definite integral as the limit of a sum, the area under the curve of the function f(x) between points a and b is being evaluated.
- As the number of subdivisions 'n' increases, the accuracy of the evaluation also increases, providing a better approximation of the area under the curve.
- Increasing the number of subdivisions 'n' improves the accuracy of the evaluation by providing more precise sums and reducing the width of each part, allowing for a more accurate estimation of the area under the curve.
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Description
Practice solving definite integrals using the limit of a sum method with this exercise and example solved problems. Check your answers and understand the solutions step by step.
