Question

the instructions for the given integral have two parts, one for the trapezoidal rule and one for simpsons rule. complete the following parts.
\\( \int_{2}^{4} \frac{1}{s^{2}} d s \\)

b. evaluate the integral directly and find \\( \left|e_{t}\
ight| \\).
\\( \int_{2}^{4} \frac{1}{s^{2}} d s=0.25 \\)
(round to four decimal places as needed.)
\\( \left|e_{t}\
ight|=0.0045 \\)
(simplify your answer.)

c. use the formula \\( \left(\left|e_{t}\
ight| /(\text { true value })\
ight) \times 100 \\) to express \\( \left|e_{t}\
ight| \\) as a percentage of the integrals true value.
\\( \left|e_{t}\
ight| \\) as a percentage of the integrals true value is \\( \square \\% \\).
(round to two decimal places as needed.)

Explanation:

Step1: Substitute values into formula

We know \(|E_T| = 0.0045\) and the true - value of the integral is \(0.25\). The formula to find the percentage is \(\frac{|E_T|}{\text{true value}}\times100\).
Substitute \(|E_T| = 0.0045\) and true - value \(=0.25\) into the formula: \(\frac{0.0045}{0.25}\times100\).

Step2: Calculate the fraction

First, calculate \(\frac{0.0045}{0.25}\). Using the rule of dividing decimals \(\frac{0.0045}{0.25}=\frac{0.0045\times4}{0.25\times4}=\frac{0.018}{1}=0.018\).

Step3: Calculate the percentage

Then, multiply the result by \(100\): \(0.018\times100 = 1.8\).

Answer:

\(1.80\)