Question

A path is traversed consecutively through three points (2,4),(5,7.6),(8,3) using a quadratic polynomial. Estimate the length of the path. Use the following Simpson's 1/3 rd rule approximation to estimate an integral.

∫ᵃᵦ f(x)dx≅(b−a)/6[f(a)+4f(a+b/2)+f(b)]
Use only MATLAB to do this problem

Answer 1

To estimate the length of a path traversed through three points using a quadratic polynomial, use Simpson's 1/3 rule approximation. Evaluate the integral of the function representing the path and multiply it by the speed to estimate the length. Use MATLAB for the calculations.

Step-by-step explanation:

Estimating the Length of a Path using Simpson's 1/3 Rule Approximation

To estimate the length of the path traversed through three points using a quadratic polynomial, we can use Simpson's 1/3 rule approximation. First, we need to evaluate the integral of the function that represents the path. Let's denote the three points as (x1, y1), (x2, y2), and (x3, y3). Then, the integral can be approximated as (∫ᵃᵦ f(x)dx) ≅ (b−a)/6 * [f(a) + 4f(a+b/2) + f(b)]. Replace f(x) with the quadratic polynomial and plug in the given points to calculate the length of the path.

In this specific problem, the three points are (2, 4), (5, 7.6), and (8, 3). We will find the integral using Simpson's 1/3 rule approximation, and then multiply it by the speed to estimate the length of the path. You can use MATLAB to perform these calculations.