Solved: Trapezoid Rule approximations Find the indicated

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

ISBN: 9780321570567 2

Solution for problem 16E Chapter 7.6

Calculus: Early Transcendentals | 1st Edition

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Problem 16E

Trapezoid Rule approximations

Find the indicated Trapezoid Rule approximations to the following integrals.

using n = 2, 4, and 8 subintervals

Step-by-Step Solution:

Problem 16E

Trapezoid Rule approximations Find the indicated Trapezoid Rule approximations to the following integrals.

$\int\limits_{1}^{9}{x}^{3}dx$ using n = 2, 4, and 8 subintervals

Step 1:

By Trapezoidal rule we have to find the integral $\int\limits_{1}^{9}{x}^{3}dx$ using 2,4,8 subintervals

Step 2:

Trapezoidal Rule

$\int\limits_{a}^{b}f(x)$ dx ≈ $\frac{\Delta{}\ x}{2}({y}_{0}+2{y}_{1}+2{y}_{2}+....+2{y}_{n-1}+{y}_{n})$

Where

$\Delta{}x=\frac{b-a}{n}$

Step 3:

Here y=f(x)= ${x}^{3}\ \ ,a=1\ \ ,b=9$

(i) for n=2

$\Delta{}x=\frac{b-a}{n}=\frac{9-1}{2}\ =4$

For x=1 y= ${1}^{3}=1$

x=5 y= ${5}^{3}=125$

x=9 y= ${9}^{3}=729$

Therefore

$\int\limits_{1}^{9}{x}^{3}dx$ = $\frac{4}{2}(1+2\ .125+729)$

$=2(1+250+729)$

$=1960$

Step 4 of 5

Chapter 7.6, Problem 16E is Solved

Step 5 of 5

Textbook: Calculus: Early Transcendentals

Edition: 1

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

ISBN: 9780321570567

This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This full solution covers the following key subjects: approximations, trapezoid, rule, Integrals, indicated. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The full step-by-step solution to problem: 16E from chapter: 7.6 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 16E from 7.6 chapter was answered, more than 313 students have viewed the full step-by-step answer. The answer to “Trapezoid Rule approximations Find the indicated Trapezoid Rule approximations to the following integrals. using n = 2, 4, and 8 subintervals” is broken down into a number of easy to follow steps, and 21 words.