Longitud de arco y área de la superficie de ecuaciones paramétricas
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Topic Notes
Si la curva está definida por las ecuaciones paramétricas: x=f(t), y=g(t) y el valor de t está incrementando de α a β, entonces podemos decir que la fórmula para la longitud de la curva paramétrica es:
L=∫αβ(dtdx)2+(dtdy)2dt
Y la fórmula para encontrar el área de la superficie es muy similar.
Si la curva está rotando con respecto de eje x, donde f′,g′ son continuas y g(t)≥0, entonces la fórmula para el área de la superficie de la curva es:
SA=∫αβ2πy(dtdx)2+(dtdy)2dt
Y la fórmula para encontrar el área de la superficie es muy similar.
Si la curva está rotando con respecto de eje x, donde f′,g′ son continuas y g(t)≥0, entonces la fórmula para el área de la superficie de la curva es:
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