MYMathApps: Calculus

5. Numerical Integration - Contents

1. Approximation Techniques

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   1. Approximation Techniques

2. Left, Right, and Middle Riemann Sums

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   1. Left, Right, and Middle Riemann Sums
   2. Example with a Known Antiderivative
   3. Example with an Unknown Antiderivative
   4. Example with Tabular Data

3. Trapezoid Rule

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   1. Trapezoid Rule
   2. Example with a Known Antiderivative
   3. Example with an Unknown Antiderivative
   4. Example with Tabular Data

4. Simpson's Rule

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   1. Simpson's Rule
      1. Area of the Best Fit Parabola - Proof
   2. Example with a Known Antiderivative
   3. Example with an Unknown Antiderivative
   4. Example with Tabular Data

5. Error Bounds

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   1. Mean Value Theorems
      1. \(2^\text{nd}\) Degree Proof
      2. Higher Degree Proof
   2. Left and Right Riemann Sums
      1. Left Riemann Sum Proof
      2. Right Riemann Sum Proof
   3. Trapezoid Rule and Middle Riemann Sum
      1. Examples to Bound the Error
      2. Examples to Guarantee a Bound
   4. Simpson's Rule
      1. Examples to Bound the Error
      2. Examples to Guarantee a Bound

6. Exercises

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   1. Exercises

7. Homework

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   1. Homework