dxUse Simpson's method to evaluate% x² +9.2Hence estimate error.

Answered: dx Use Simpson's method to evaluate o…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter0: Preparing For Algebra

Section: Chapter Questions

Problem 34PRT

See similar textbooks

Related questions

Question

dx
Use Simpson's method to evaluate
% x² +9
.2
Hence estimate error.

Expert Solution

Step 1

In this question first, we have to evaluate the integral through normal integration and find the value. Then we have to use the Simpsons method to evaluate the integral. After that, we should compare the two values obtained from these two different methods to estimate the error.

Step 2

First, we have to find the original or exact value using normal integration methods.

$\int_{0}^{2} d x / (x^{2} + 9)$ = $\int_{0}^{2} d x / 9 (x^{2} / 9 + 1)$ = $1 / 9 \int_{0}^{2} d x / (x^{2} / 9 + 1)$ = $1 / 9 \int_{0}^{2} d x / ({(x / 3)}^{2} + 1)$

Take u = x/3, then du = 1/3dx, This gives 3du = dx

So our integral becomes $1 / 9 \int_{0}^{2} 3 d u / (u^{2} + 1)$ = 3/9 $\int_{0}^{2} d u / (1 + u^{2})$

We know $\int 1 / (1 + x^{2}) d x = \tan^{- 1} (x)$

So, $3 / 9 \int_{0}^{2} d u / (1 + u^{2}) = 1 / 3 {[\tan^{- 1} u]}_{0}^{2} = 1 / 3 {[\tan^{- 1} (x / 3)]}_{0}^{2}$

1/3tan^-1(2/3) - 1/3tan^-1(0/3) = 1/3tan^-1(2/3) =1/3 * 0.5880026035 ( in radians) = 0.1960008678

Step by step

Solved in 4 steps

Knowledge Booster

$Basics (types, similarity, etc)$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions