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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Answer to a math 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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92 Answers
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. Evaluamos f(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

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