**Trapezoidal and Simpson's Rule Integration Accuracy**### Trapezoidal Rule**Objective:**Determine the value of $ n $ needed to approximate the integral of the function \[ \int_{3}^{8} (-x^4 + 22x^3 - 144x^2 - 3x + 5) \, dx \]using the Trapezoidal Rule with accuracy within 0.1.- **Answer:** $ n = $ [Enter value]### Simpson's Rule**Objective:**Determine the value of $ n $ needed to approximate the integral of the same function using Simpson's Rule with accuracy within 0.1.- **Answer:** $ n = $ [Enter value]**Hint:** Ensure your answers are whole numbers. Simpson's Rule requires $ n $ to be an even number.

Answered: How large should n be to guarantee that…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

**Trapezoidal and Simpson's Rule Integration Accuracy**

### Trapezoidal Rule

**Objective:**
Determine the value of $ n $ needed to approximate the integral of the function
\[ \int_{3}^{8} (-x^4 + 22x^3 - 144x^2 - 3x + 5) \, dx \]
using the Trapezoidal Rule with accuracy within 0.1.

- **Answer:** $ n = $ [Enter value]

### Simpson's Rule

**Objective:**
Determine the value of $ n $ needed to approximate the integral of the same function using Simpson's Rule with accuracy within 0.1.

- **Answer:** $ n = $ [Enter value]

**Hint:** Ensure your answers are whole numbers. Simpson's Rule requires $ n $ to be an even number.

Expert Solution

Step 1: Introduction

(a)

How large should n be to guarantee that the Trapezoidal Rule approximation

$integral subscript 3 superscript 8 open parentheses negative x to the power of 4 plus 22 x cubed minus 144 x squared minus 3 x plus 5 close parentheses d x$ to is accurate to within 0.1.

(b)

How large should n be to guarantee that the Simpson's Rule approximation to:

$integral subscript 3 superscript 8 open parentheses negative x to the power of 4 plus 22 x cubed minus 144 x squared minus 3 x plus 5 close parentheses d x$ is accurate to within 0.1.