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Quiz de Cálculo II – Apps de Matemáticas

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Quiz de Cálculo II – Apps de Matemáticas

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Integral, áreas y sumatorias

Created by

Ana Maria Hernández
Ana Maria Hernández
Mexico

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Quiz de Cálculo II – Apps de Matemáticas
 

Quiz de Cálculo II – Apps de MatemáticasOnline version

Integral, áreas y sumatorias

by Ana Maria Hernández
1

¿Qué representa una integral definida ∫f(x) dx en geometría?

2

¿Qué es una integral indefinida?

3

¿Qué método se usa para calcular áreas con sumas de Riemann?

4

Definición de suma de Riemann: ¿qué componente es Δx?

5

¿Qué condición garantiza que el límite de las sumas de Riemann exista para f continua?

6

Propiedad de las integrales: linealidad de ∫ (af(x)+bg(x)) dx

7

Calculando área: ¿Qué expresión representa el área entre y = f(x) y el eje x desde a hasta b?

8

Propiedad de sumas de Riemann: si f es no negativa, la suma de Riemann converge a...

9

¿Qué diferencia una integral definida de una suma de Riemann?

Explicación

La integral definida mide el área (considerando signo) bajo la curva entre a y b.

La integral indefinida devuelve F(x) + C, donde F'(x)=f(x).

Las sumas de Riemann aproximan áreas con particiones y puntos de muestra, luego se toma límite.

Δx es la anchura de cada subintervalo en la partición del dominio.

Si f es continua en [a,b], la integral definida existe y es finita.

La integral es lineal: puede distribuirse y factorizar constantes.

Si f puede ser negativa, se usa valor absoluto para área positiva.

Para f no negativa y continua, la suma de Riemann converge al valor de ∫_a^b f(x) dx.

La integral definida es el límite cuando la partición se refina; la suma de Riemann es la aproximación finita.

 
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