Trapezoidal Rule & Simpsons Rule AP Calculus Mrs. Mongold.

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Presentation transcript:

Trapezoidal Rule & Simpsons Rule AP Calculus Mrs. Mongold

What is the antiderivative of …

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

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?

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!

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

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.

The Trapezoidal Rule

Example

Evaluate Using Antiderivative

Verify your approximation with your calculator

Homework