- #1
pari786
- 29
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why do we use n as even number with simpson's rule ?
Simpson's Rule is a mathematical method for approximating the area under a curve by dividing it into multiple smaller sections and using a quadratic function to estimate the area of each section. It is commonly used to calculate integrals when the function's derivative is not known.
Unlike other numerical integration methods, Simpson's Rule uses a quadratic function to estimate the area under a curve, which results in a more accurate approximation compared to methods that use linear functions.
Simpson's Rule can be applied to any function that is continuous and has a known derivative. It is not limited to only even N, as it can also be used for odd N.
The number of sections, or subintervals, used in Simpson's Rule depends on the desired level of accuracy. Generally, the more sections that are used, the more accurate the approximation will be.
The formula for calculating even N with Simpson's Rule is:
∫ab f(x) dx ≈ (b-a)/3n [f(a)+2∑i=1n/2-1 f(a+2i(b-a)/n) + 4∑i=1n/2 f(a+(2i-1)(b-a)/n) + f(b)]
Where a and b are the lower and upper limits of the integral, n is the number of subintervals, and f(x) is the function being integrated.