Simpson's Rule
Definition
Simpson's Rule is a numerical integration method used to approximate the definite integral of a function. It divides the interval into multiple subintervals and uses quadratic polynomials to estimate the area under the curve.
Analogy
Imagine you have a curved slide in a playground, and you want to find out how much water it can hold. Instead of measuring every single drop, you divide the slide into smaller sections and use quadratic buckets to estimate the total amount of water it can hold.
Related terms
Trapezoidal Rule: The Trapezoidal Rule is another numerical integration method that approximates the definite integral by dividing the interval into subintervals and using trapezoids instead of quadratic polynomials.
Riemann Sum: A Riemann Sum is an approximation method for finding definite integrals by dividing an interval into subintervals and using rectangles to estimate the area under a curve.
Numerical Integration: Numerical Integration refers to methods used to approximate definite integrals when an antiderivative cannot be found analytically. These methods involve dividing intervals and using geometric shapes or polynomials to estimate areas.
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