# How does Simpson's Rule work?

Let us approximate the definite integral

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Simpson's Rule is a numerical method used for approximating the definite integral of a function. It works by dividing the interval of integration into an even number of subintervals and approximating the area under the curve within each subinterval using quadratic polynomials. These quadratic polynomials are obtained by interpolating the function at three points: the endpoints of each subinterval and their midpoint. Simpson's Rule formula involves calculating the weighted sum of these quadratic approximations over all the subintervals. The weights are determined by a specific pattern depending on the number of subintervals used. This method provides a more accurate approximation of the integral compared to simpler methods like the Trapezoidal Rule, especially for functions that are well-behaved and smooth over the interval of integration.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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