4.6 Numerical Integration Trapezoid and Simpson’s Rules.

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Presentation transcript:

4.6 Numerical Integration Trapezoid and Simpson’s Rules

Trapezoidal Rule To estimate the definite integral, we will divide the Interval into “n” trapezoids.

The Trapezoidal Rule Let f be a continuous function on [a,b]. Then the Trapezoidal Rule for estimating the definite integral is given by

Use the Trapezoid Rule to approximate the definite integral for the given “n”.

Use the Trapezoid Rule to approximate the definite integral. Compare results when n=3 and n=6

Simpsons Rule (with an even “n”) Let f be a continuous function on [a,b]. Simpson’s Rule for estimating the definite integral is given by

Use Simpsons Rule to approximate

HOMEWORK Pg 314: 2-14even, 19