Math Problem Statement

Dame el área entre dos curvas de las siguientes funciones: y=√(x+2), y=1/(x+1), con x=2

Solution

Para calcular el área entre dos curvas, seguimos estos pasos:

  1. Encontrar los puntos de intersección: Determinamos los límites de integración.
  2. Identificar cuál función está arriba: Esto nos asegura que calculamos el área correctamente.
  3. Establecer y resolver la integral: Integramos la diferencia de las funciones.

Paso 1: Encontrar los puntos de intersección

Las funciones dadas son:
y=x+2yy=1x+1.y = \sqrt{x + 2} \quad \text{y} \quad y = \frac{1}{x + 1}.

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Math Problem Analysis

Mathematical Concepts

Calculus
Definite Integrals
Area Between Curves

Formulas

Area = ∫[a, b] (f(x) - g(x)) dx
Intersection points: Solve f(x) = g(x)

Theorems

Fundamental Theorem of Calculus

Suitable Grade Level

Undergraduate or Advanced High School (Grades 11-12)

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