Question

Approximate the area under the curve 𝑓(𝑥) = 𝑥 on the interval [0,2] using a sum of Riemann midpoint with 4 subintervals.

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Jett

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1. Calculamos el ancho de los subintervalos:

\Delta x = \frac{2-0}{4} = 0.5

2. Determinamos los puntos medios de cada subintervalo:

x_1 = 0.25, \ x_2 = 0.75, \ x_3 = 1.25, \ x_4 = 1.75

3. Evaluamosf(x) en cada punto medio:

f(0.25) = 0.25

f(0.75) = 0.75

f(1.25) = 1.25

f(1.75) = 1.75

4. Calculamos la suma de las áreas de los rectángulos:

\text{Área} \approx (0.25 + 0.75 + 1.25 + 1.75) \cdot 0.5

5. Realizamos la suma:

0.25 + 0.75 + 1.25 + 1.75 = 4

6. Multiplicamos por\Delta x :

\text{Área} \approx 4 \cdot 0.5 = 2

7. Resultado:

\text{Área} \approx 2

2. Determinamos los puntos medios de cada subintervalo:

3. Evaluamos

4. Calculamos la suma de las áreas de los rectángulos:

5. Realizamos la suma:

6. Multiplicamos por

7. Resultado:

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