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4.6 Numerical Integration
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The Trapezoidal Rule
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One method to approximate a definite integral is to use n trapezoids.
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The Trapezoidal Rule
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Example:
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Simpson’s Rule One way to view the trapezoidal rule if to say that on each subinterval, you approximate f by a 1 st degree polynomial. In Simpson’s Rule, you approximate f by a 2 nd degree polynomial.
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Simpson’s Rule For Simpson’s Rule, we are still going to partition [a,b] into n subintervals, but n must be even! We will look at 2 subintervals at a time and create a 2 nd degree polynomial, p, that passes through (x o, y o ), (x 1, y 1 ), and (x 2, y 2 ). Then,
![Simpson’s Rule For Simpson’s Rule, we are still going to partition [a,b] into n subintervals, but n must be even.](http://images.slideplayer.com/22/6419605/slides/slide_9.jpg "We will look at 2 subintervals at a time and create a 2 nd degree polynomial, p, that passes through (x o, y o ), (x 1, y 1 ), and (x 2, y 2 ). Then,.")
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Example:
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