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4.6 Numerical Integration Trapezoid and Simpson’s Rules
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Trapezoidal Rule To estimate the definite integral, we will divide the Interval into “n” trapezoids.
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The Trapezoidal Rule Let f be a continuous function on [a,b]. Then the Trapezoidal Rule for estimating the definite integral is given by
![The Trapezoidal Rule Let f be a continuous function on [a,b].](http://images.slideplayer.com./22/6419604/slides/slide_4.jpg "Then the Trapezoidal Rule for estimating the definite integral is given by.")
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Use the Trapezoid Rule to approximate the definite integral for the given “n”.
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Use the Trapezoid Rule to approximate the definite integral. Compare results when n=3 and n=6
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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
![Simpsons Rule (with an even n ) Let f be a continuous function on [a,b].](http://images.slideplayer.com./22/6419604/slides/slide_8.jpg "Simpson’s Rule for estimating the definite integral is given by.")
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Use Simpsons Rule to approximate
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HOMEWORK Pg 314: 2-14even, 19
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