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

the estimate using the trapezoidal rule with ( n = 4 ) is 0.2545
(round to four decimal places as needed.)

the upper bound for ( left|e_{t}
ight| ) is 0.0156
(round to four decimal places as needed.)

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|=square
(simplify your answer.)

Explanation:

Step1: Recall the formula for \(|E_T|\)

\(|E_T|=\text{Estimated value}-\text{Actual value}\)

Step2: Substitute the values

We know the estimated value using the trapezoidal rule is \(0.2545\) and the actual value of the integral \(\int_{2}^{4}\frac{1}{s^{2}}ds = 0.25\)

So, \(|E_T|=|0.2545 - 0.25|\)

Step3: Calculate the result

\(|E_T|=0.0045\)

Answer:

\(0.0045\)