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_{0}^{\\pi} \\sin t d t \\)\n\\( t \\approx 1.8961 \\)\n(round to four decimal places as needed.)\nan upper bound for \\( \\left|e_{t}\\right| \\) is 0.1615.\n(round to four decimal places as needed.)\nb. evaluate the integral directly and find \\( \\left|e_{t}\\right| \\).\n\\( \\int_{0}^{\\pi} \\sin d t=2 \\)\n(type an exact answer in simplified form.)\n\\( \\left|e_{t}\\right|=\\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_{0}^{\\pi} \\sin t d t \\)\n\\( t \\approx 1.8961 \\)\n(round to four decimal places as needed.)\nan upper bound for \\( \\left|e_{t}\\right| \\) is 0.1615.\n(round to four decimal places as needed.)\nb. evaluate the integral directly and find \\( \\left|e_{t}\\right| \\).\n\\( \\int_{0}^{\\pi} \\sin d t=2 \\)\n(type an exact answer in simplified form.)\n\\( \\left|e_{t}\\right|=\\square \\)\n(round to four decimal places as needed.)

Answer

Explanation:

Step1: Recall the formula for (|E_T|)

(|E_T|=\vert\text{Exact Value}-\text{Trapezoidal Approximation}\vert)

Step2: Substitute the values

The exact value of (\int_{0}^{\pi}\sin tdt = 2) and the trapezoidal approximation (T\approx1.8961) (|E_T|=\vert2 - 1.8961\vert)

Step3: Calculate the result

(|E_T|=2- 1.8961=0.1039)

Answer:

(0.1039)