Simpson's Rule finds its application in various fields such as physics, engineering, economics, and more. So using Simpson's Rule, the value of the integral $$$\int_0^2\left(x^3+2x\right)dx $$$ is approximately $$$5.53125 $$$. The formula for approximating the definite integral using Simpson's Rule is as follows: $$\int_a^b f(x) dx \approx \frac\left(0+4(0.375)+2(3)+4(8.625)+16\right)\approx5.53125 $$ Simpson's Rule is derived from the idea that a curve can be approximated using a quadratic polynomial over small intervals. Simpson’s Rule Formula and Calculation Process These curves give us more accurate results. Instead of using straight lines like other methods, it uses curved lines called quadratic polynomials. Simpson's Rule is a way to find a good estimate for integrals. The rule is an extension of the trapezoidal rule, but it achieves a higher degree of accuracy by using quadratic polynomial approximations. Simpson's Rule is named after the mathematician Thomas Simpson and is based on the principle of approximating the area under a curve by dividing it into smaller sections and fitting parabolic curves to each section. This practical approach will make it easier for students to learn and practice integral approximation. In this article, we'll learn about Simpson's Rule and how it can be used to approximate integrals. Luckily, there's a method called Simpson's Rule that helps us estimate integrals. Integrals are important in math, engineering, and science, but solving them can be tough. Simpson's Rule: An Easy Approach to Approximating Integrals Introduction
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