77Evaluateds using the trapezoidal rule and Simpson's rule. DetermineThe value ofds is 1.7143.11(Round to four decimal places as needed.)i. the value of the integral directly.ii. the trapezoidal rule estimate for n = 4.iii. an upper bound for E-.72The trapezoidal rule estimate ofds for n = 4 is 2.2973.2iv. the upper bound for ETas a percentage of the integral's true value.1v. the Simpson's rule estimate for n = 4.vi. an upper bound for Es.(Round to four decimal places as needed.)The upper bound on E- isvii. the upper bound for Esas a percentage of the integral's true value.(Round to four decimal places as needed.)

The given integral is ∫172s2ds (1) Using property of definite integral we have…

Answered: The value of ds is 1.7143. |(Round to…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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7
7
Evaluate
ds using the trapezoidal rule and Simpson's rule. Determine
The value of
ds is 1.7143.
1
1
(Round to four decimal places as needed.)
i. the value of the integral directly.
ii. the trapezoidal rule estimate for n = 4.
iii. an upper bound for E-.
7
2
The trapezoidal rule estimate of
ds for n = 4 is 2.2973.
2
iv. the upper bound for ET
as a percentage of the integral's true value.
1
v. the Simpson's rule estimate for n = 4.
vi. an upper bound for Es.
(Round to four decimal places as needed.)
The upper bound on E- is
vii. the upper bound for Es
as a percentage of the integral's true value.
(Round to four decimal places as needed.)

Expert Solution

Step 1

The given integral is $\int_{1}^{7} \frac{2}{s^{2}} d s$

(1) Using property of definite integral we have

$\begin{array}{rcl} \int_{1}^{7} \frac{2}{s^{2}} d s & = & 2 {(\frac{- 1}{s})}_{1}^{7} \\ = & - 2 (\frac{1}{7} - 1) \\ = & - 2 \times \frac{- 6}{7} \\ = & \frac{12}{7} \\ = & 1.714 \end{array}$

(2) Trapezoidal rule

$\int_{a}^{b} f (x) d x = \frac{h}{2} [\{f (x_{0}) + f (x_{n})\} + 2 \{f (x_{1}) + f (x_{2}) + . . . + f (x_{n})\}]$

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