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Identificación de u y dv en por partes

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Identificación de u y dv en por partes

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Elección correcta de u y dv

Created by

Karina Santos
Karina Santos
Mexico

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Identificación de u y dv en por partes
 

Identificación de u y dv en por partesOnline version

Elección correcta de u y dv

by Karina Santos
1

Al ∫ x e^x dx, ¿qué debe ser u para facilitar la integración por partes?

2

En ∫ x sin x dx, elegir u adecuado es:

3

¿Qué se debe hacer con u y dv tras escoger?

4

En ∫ e^x cos x dx, una buena elección es:

5

Si ∫ x^2 e^x dx, ¿qué dv es razonable?

6

En ∫ x/(x+1) dx, ¿una opción adecuada para u?

7

Para ∫ (ln x)^2 dx, elegir dv como:

8

En ∫ x e^{2x} dx, u debe ser:

9

¿Qué resultado espera tras aplicar integración por partes?

Explicación

Correcto: x facilita derivar a 1 y mantener e^x integrable.

Correcto: derivar x reduce alinea la integral.

Correcto: se pronostica du = u' dx y v = ∫ dv.

Incorrecto: mejor usar u = cos x para derivar y reducir.

Correcto: e^x es fácil de integrar; du = 2x dx.

Correcto: derivar x es 1; simplifica la fracción.

Correcto: dv = dx facilita la integral de du = 2 ln x / x.

Correcto: derivar x simplifica la iteración.

Correcto: fórmula estándar: ∫ u dv = uv - ∫ v du.

 
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