Encontrando el área dado el rango del parámetro
Encuentra el área bajo la curva paramétrica definida por x=t2+1y=t3+t2+4, donde 1≤t≤3. Asume que la curva está trazada perfectamente de izquierda a derecha para el rango del parámetro t.
Encuentra el área dentro de la curva paramétrica dada por x=acos(θ), y=bsen(θ), donde 0≤θ≤2π y a,b son constantes.
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Sabemos que el área bajo la curva de a a b se obtiene con ∫abf(x)dx. ¿Pero qué hacemos cuando tenemos ecuaciones paramétricas?
Si la curva se define con las ecuaciones paramétricas: x=f(t), y y=g(t) y el valor de t va incrementando de α
a β, entonces el área bajo la curva paramétrica es:
A=∫abydx=∫αβg(t)f′(t)dt
Pero si el valor de t va incrementando de β a α entonces el área bajo la curva paramétrica es:
A=∫abydx=∫βαg(t)f′(t)dt
Así que asegúrate de saber cuál de las dos ecuaciones usar.