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Problem 28 Hard Difficulty

Use Simpson's Rule with $ n = 10 $ to estimate the arc length of the curve. Compare your answer with the value of the integral produced by a calculator.

$ y = e^{-x^2} $ , $ 0 \le x \le 2 $

Answer

$S_{10}=2.280731$
Using Calculator, $L=2.280526$

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Video Transcript

Hey, it's clear. So when you read here So we're going to first find the derivative. We get the derivative of eat the negative X square. We got negative to x e to the negative X square. So are our Collings becomes we have to square this one Plus for X square e to the negative two x squared DX We're gonna make this to be f of X. So l is equal to into grow from 0 to 2 f of x t x Yes, we're gonna find the with using Simpsons roll to minus zero over 10 So it gives us 100.2. So using us um, sense rule we get go with Divided by three zero close for a of 0.2 plus two f of 0.4 plus four of of 0.6 plus two f 20.8 plus four f of one It was two off of 1.2 close four f of 1.4 plus two f of 1.6 plus four off 1.8 plus effort to. And this gives us 2.28 07 31 And when we use a calculator, we get around to point to a 05 to 6, which is very close to each other