Numerical Integration

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Numerical Integration

• Section 4.6

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Why Numerical Integration?
Lets say we want to evaluate the following
definite integral

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Numerical Integration
There are many functions whose antiderivatives
cannot be found. To find the definite integral
of these functions, we will use one of the
approximation techniques.   Using Trapezoids
Area of a trapezoid A
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Trapezoid Rule
Pattern The coefficients in the Trapezoid Rule
are 1 2 2 2 2 2 1
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Example

• Use the Trapezoid Rule to approximate the
  definite integral. (w/ n 4)

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Simpsons Rule
n is even
Pattern The coefficients in Simpsons Rule
are 1 4 2 4 2 4 2 4 1
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Example

• Use Simpsons Rule to approximate the definite
  integral.
• (w/ n 4)

Check it out on the calculator.