Hello, Please answer the following attached Calculus question correctly and show all your work completely without skipping any steps. Please write the answer in simplest form. Thanks. Use the Simpson’s Rule to approximate the given integral with n= 8. (Find S8.) Roundyour answers to six decimal places. Write answer in the simplest form.21Jo 1+x°

Given,∫0211+x6dxHere n=8, therefore h=b-anh=2-08h=14 Now we create table x 0 1/4 1/2 3/4 1 5/4…

Answered: Use the Simpson's Rule to approximate…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Hello, Please answer the following attached Calculus question correctly and show all your work completely without skipping any steps. Please write the answer in simplest form. Thanks.

Use the Simpson’s Rule to approximate the given integral with n= 8. (Find S8.) Round
your answers to six decimal places. Write answer in the simplest form.
2
1
Jo 1+x°

Expert Solution

Step 1

$G i v e n, \int_{0}^{2} \frac{1}{1 + x^{6}} d x H e r e n = 8, t h e r e f o r e h = \frac{b - a}{n} h = \frac{2 - 0}{8} h = \frac{1}{4}$

Now we create table

x	0	1/4	1/2	3/4	1	5/4	3/2	7/4	2
$\frac{1}{1 + x^{6}}$	0	0.999756	0.984615	0.848912	0.5	0.207697	0.080706	0.033644	0.015385

$W e k n o w t h a t, \int_{a}^{b} f (x) = \frac{h}{3} {(y_{0} + y_{8}) + 4 (y_{1} + y_{3} + y_{5} + y_{7}) + 2 (y_{2} + y_{4} + y_{6})} \int_{0}^{2} \frac{1}{1 + x^{6}} d x = \frac{\frac{1}{4}}{3} {(1 + 0.015385) + 4 (0.999756 + 0.848912 + 0.207697 + 0.033644) + 2 (0.984615 + 0.5 + 0.080706)} \int_{0}^{2} \frac{1}{1 + x^{6}} d x = \frac{1}{12} {1.015385 + 4 (2.090007) + 2 (1.565321)} \int_{0}^{2} \frac{1}{1 + x^{6}} d x = \frac{1}{12} {1.015385 + 8.360036 + 3.130642} \int_{0}^{2} \frac{1}{1 + x^{6}} d x = \frac{1}{12} {12.506063} \int_{0}^{2} \frac{1}{1 + x^{6}} d x = 1.0421719$