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 int_{2}^{4} \frac{1}{s^{2}} d s \ni. using the trapezoidal rule\na. estimate the integral with ( n = 4 ) steps and find an upper bound for ( left|e_{t}\right| ).\nthe estimate using the trapezoidal rule with ( n = 4 ) is 0.2545\n(round to four decimal places as needed.)\nthe upper bound for ( left|e_{t}\right| ) is 0.0156\n(round to four decimal places as needed.)\nb. evaluate the integral directly and find ( left|e_{t}\right| ).\n int_{2}^{4} \frac{1}{s^{2}} d s=square \n(round to four decimal places as needed.)

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

Answer

Explanation:

Step1: Integrate the function

The integral of (\frac{1}{s^{2}}) is (-\frac{1}{s}). $$\int_{2}^{4}\frac{1}{s^{2}}ds=\left[-\frac{1}{s}\right]_{2}^{4}$$

Step2: Apply the fundamental theorem of calculus

Substitute the upper and lower limits: $$\left(-\frac{1}{4}\right)-\left(-\frac{1}{2}\right)=-\frac{1}{4}+\frac{1}{2}$$

Step3: Simplify the expression

$$-\frac{1}{4}+\frac{1}{2}=\frac{-1 + 2}{4}=\frac{1}{4}=0.25$$

Answer:

(0.25)