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ryingling5711
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when do you use simpson's rule over trapezoidal rule?
why does simpsons rule alternate 4 and 2?
why does simpsons rule alternate 4 and 2?
ryingling5711 said:when do you use simpson's rule over trapezoidal rule?
why does simpsons rule alternate 4 and 2?
ryingling5711 said:I'm not really sure about that because i know you can use both for parabolic curves so but maybe your right that the trap rule is better for estimating integrals on less parabolic curves.
Simpson's rule is a numerical integration method used to approximate the area under a curve. It works by dividing the area into smaller segments and using a polynomial function to estimate the value of each segment. The estimated values are then summed to get an overall approximation of the area.
Both Simpson's rule and trapezoidal rule provide fairly accurate approximations of the area under a curve. However, Simpson's rule tends to be more accurate since it uses a higher order polynomial function to estimate the curve, while trapezoidal rule uses a linear function.
Simpson's rule should be used when the curve being integrated is smooth and does not have any sharp turns. This is because Simpson's rule uses a parabolic function to estimate the curve, which is a better fit for smooth curves. Trapezoidal rule, on the other hand, can be used for any type of curve but may not provide as accurate results for smooth curves.
One limitation of Simpson's rule and trapezoidal rule is that they can only be used for functions that are continuous and have a known equation. They also require a certain number of points to be calculated, which can be time-consuming for complex functions. Additionally, these methods may not be accurate for curves with very large or very small values.
Yes, there are many other numerical integration methods, such as the midpoint rule, Gaussian quadrature, and Romberg integration. Each method has its own advantages and limitations, so it's important to choose the right method for the specific function being integrated.