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Trapezoidal Rule & Simpsons Rule AP Calculus Mrs. Mongold.

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Presentation on theme: "Trapezoidal Rule & Simpsons Rule AP Calculus Mrs. Mongold."— Presentation transcript:

1 Trapezoidal Rule & Simpsons Rule AP Calculus Mrs. Mongold

2 What is the antiderivative of …

3 Would you agree…There is no elementary function that has any of these functions as its derivative?

4 What is the antiderivative of … Would you agree…There is no elementary function that has any of these functions as its derivative? Does this mean we can’t Evaluate a definite integral Involving a function whose Antiderivative cannot be found?

5 What is the antiderivative of … Would you agree…There is no elementary function that has any of these functions as its derivative? Does this mean we can’t Evaluate a definite integral Involving a function whose Antiderivative cannot be found? Of course not!

6 Approximation Techniques  LRAM, RRAM, and MRAM allow us to approximate using rectangles

7 Approximation Techniques  LRAM, RRAM, and MRAM allow us to approximate using rectangles  Today we are going to look at Trapezoidal Rule (even better than rectangular approximation) and Simpsons Rule.

8 The Trapezoidal Rule

9 Example

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16 Evaluate Using Antiderivative

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19 Verify your approximation with your calculator

20 Homework

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