Estimate the minimum number of subintervals to approximate the value of 7x+3 dx with an error of magnitude less than 2x 10* using -4 a. the error estimate formula for the Trapezoidal Rule. b. the error estimate formula for Simpson's Rule. The minimum number of subintervals using the Trapezoidal Rule is (Round up to the nearest whole number.)

Estimate the minimum number of subintervals to approximate the value of 7x+3 dx with an error of magnitude less than 2x 10* using -4 a. the error estimate formula for the Trapezoidal Rule. b. the error estimate formula for Simpson's Rule. The minimum number of subintervals using the Trapezoidal Rule is (Round up to the nearest whole number.)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 90E

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.

Question

3
Estimate the minimum number of subintervals to approximate the value of
7x + 3 dx with an error of magnitude less than 2x 10
- 4
using
a. the error estimate formula for the Trapezoidal Rule.
b. the error estimate formula for Simpson's Rule.
The minimum number of subintervals using the Trapezoidal Rule is
(Round up to the nearest whole number.)

Expert Solution

Step 1

To estimate the error for the $\int_{0}^{3} \sqrt{7 x + 3} d x$ with an error of magnitude less than $2 \times 10^{- 4}$ using

(a) Trapezoidal rule

(b) Simpson's rule.

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