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miskamm [114]
3 years ago
13

¿En que orden se deben escribir las funciones, para aplicar la integral definida cuando se desea calcular el área?

Mathematics
1 answer:
lozanna [386]3 years ago
7 0

Answer:

Si querés calcular el área entre las funciones f(x) y g(x) en el rango (a, b), usualmente se calcula la integral de la función más grande en el intervalo menos la función más pequeña en el intervalo, es decir, si:

f(x) > g(x) para todo x ∈ (a, b)

Entonces calculamos:

\int\limits^b_a {(f(x) - g(x))} \, dx

Puesto que el área se define como la encerrada por las dos curvas, y si lo hiciéramos de otro modo, las curvas no encerrarían ningun área.

Ahora, si no se cumple lo anterior, es decir, g(x) > f(x) en algún dado intervalo, entonces separamos la integral en distintas partes de tal forma que siempre definamos un área positiva.

es decir, si:

f(x) ≥ g(x)  para x ∈ (a, n)

g(x) ≥ f(x) para x ∈ (n, b)

entonces el área estará dada por:

\int\limits^n_a {f(x) - g(x)}dx \, +\int\limits^b_n {g(x) - f(x)} \, dx

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