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…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter5: Exponential And Logarithmic Functions

Section5.CR: Chapter Review

Problem 16E: Find the intensity of light at a depth of 12 meter if I0=14 and k=0.7. Round to two decimals.

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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

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