the instructions for the given integral have two parts, one for the trapezoidal rule and one for simpsons…

the instructions for the given integral have two parts, one for the trapezoidal rule and one for simpsons rule. complete the following parts.\n\n int_{2}^{4} \frac{1}{s^{2}} d s \n\nthe estimate using the trapezoidal rule with ( n = 4 ) is 0.2545\n(round to four decimal places as needed.)\n\nthe upper bound for ( left|e_{t}\right| ) is 0.0156\n(round to four decimal places as needed.)\n\nb. evaluate the integral directly and find ( left|e_{t}\right| ).\n\n int_{2}^{4} \frac{1}{s^{2}} d s = 0.25 \n(round to four decimal places as needed.)\n\n left|e_{t}\right|=square \n(simplify your answer.)

the instructions for the given integral have two parts, one for the trapezoidal rule and one for simpsons rule. complete the following parts.\n\n int_{2}^{4} \frac{1}{s^{2}} d s \n\nthe estimate using the trapezoidal rule with ( n = 4 ) is 0.2545\n(round to four decimal places as needed.)\n\nthe upper bound for ( left|e_{t}\right| ) is 0.0156\n(round to four decimal places as needed.)\n\nb. evaluate the integral directly and find ( left|e_{t}\right| ).\n\n int_{2}^{4} \frac{1}{s^{2}} d s = 0.25 \n(round to four decimal places as needed.)\n\n left|e_{t}\right|=square \n(simplify your answer.)

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)