Question
Determine the mass and centroid of a sheet of uniform density p, which is limited by the function f (x) =, the x-axis and the line x = 4
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Answer to a math question Determine the mass and centroid of a sheet of uniform density p, which is limited by the function f (x) =, the x-axis and the line x = 4
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4.8113 Answers
1. Calcular la masa: M = p \int_{0}^{4} f(x) \, dx
2. Calcular las coordenadas del centroide:\bar{x} = \frac{1}{M} \int_{0}^{4} x f(x) \, dx
3. Calcular:\bar{y} = \frac{1}{2M} \int_{0}^{4} f(x)^2 \, dx
Respuesta: La masa esM = p \int_{0}^{4} f(x) \, dx \left(\bar{x}, \bar{y}\right) \bar{x} = \frac{1}{M} \int_{0}^{4} x f(x) \, dx \bar{y} = \frac{1}{2M} \int_{0}^{4} f(x)^2 \, dx
2. Calcular las coordenadas del centroide:
3. Calcular:
Respuesta: La masa es
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