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Cálculo de Integrales: Quiz

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Cálculo de Integrales: Quiz

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Quiz de cálculo integral

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Aula 11 Bachillerato
Aula 11 Bachillerato
Mexico

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Cálculo de Integrales: Quiz
 

Cálculo de Integrales: QuizOnline version

Quiz de cálculo integral

by Aula 11 Bachillerato
1

1) ¿Qué regla permite ∫ u dv = uv − ∫ v du?

2

2) ¿Qué teorema relaciona ∫_a^b f'(x) dx con f(b)-f(a)?

3

3) Evalúa ∫ x dx.

4

4) ¿Qué técnica resuelve ∫ 2x cos(x^2) dx?

5

5) ∫ (2x)/(x^2+1) dx se evalúa como:

6

6) ¿Converge ∫_1^∞ 1/x^2 dx?

7

7) ∫ sin^2 x dx se escribe como:

8

8) ¿Cuál es la antiderivada de e^{2x}?

9

9) ∫ sec^2 x dx = ?

10

10) Evalúa ∫_0^π sin x dx.

Explicación

La integración por partes es la técnica para ese tipo de integrales.

El Fundamental del Cálculo conecta derivadas e integrales.

La antiderivada de x es x^2/2 más constante.

Con u = x^2, du = 2x dx simplifica la integral.

Derivada de ln(x^2+1) es 2x/(x^2+1).

∫_1^∞ x^-2 dx = [−1/x]_1^∞ = 1.

Usa la identidad sin^2 x = (1−cos 2x)/2.

La derivada de e^{2x} es 2e^{2x}, por eso 1/2 factor.

La derivada de tan x es sec^2 x.

La integral de sin x en [0,π] es 2.

 
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