Cálculo integral

Cálculo integral

12th Grade

8 Qs

quiz-placeholder

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Cálculo integral

Cálculo integral

Assessment

Quiz

Mathematics

12th Grade

Practice Problem

Hard

Created by

Ana Cristina Ruiz

Used 22+ times

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8 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

 F(x)F\left(x\right)  es una función primitiva de  f(x)f\left(x\right)\Longleftrightarrow  

 F(x)=f(x)F'\left(x\right)=f\left(x\right)  

 f(x)=F(x)f'\left(x\right)=F\left(x\right)  

 F\left(x\right)=f\left(x\right)+C  

 F(x)=f(x)F\left(x\right)=f\left(x\right)  

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Si  c[a,b]c\in\left[a,b\right]  ,  abf(x)dx=acf(x)dx+cbf(x)dx\int_a^bf\left(x\right)dx=\int_a^cf\left(x\right)dx+\int_c^bf\left(x\right)dx  

Verdadero

Falso

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

 abf(x)dx=\int_a^bf\left(x\right)dx=  

 baf(x)dx-\int_b^af\left(x\right)dx  

 baf(x)dx\int_b^af\left(x\right)dx  

4.

MULTIPLE SELECT QUESTION

30 sec • 1 pt

Media Image

SEÑALA TODAS LAS RESPUESTAS CORRECTAS:

Halla el área limitada por la curva  y=x^3-6x^2+8x  y el eje  OXOX  

 0\ u^2  

 8 u28\ u^2  

Media Image
Media Image

 04(x36x2+8x)dx\int_0^4\left(x^3-6x^2+8x\right)dx​  

5.

MULTIPLE SELECT QUESTION

30 sec • 1 pt

Media Image

SEÑALA TODAS LAS RESPUESTAS CORRECTAS:

Halla el área encerrada entre el eje de abscisas y las parábolas   f(x)=x2f\left(x\right)=x^2  y  g(x)=x24x+4g\left(x\right)=x^2-4x+4  

 01x2dx+12(x24x+4)dx\int_0^1x^2dx+\int_1^2\left(x^2-4x+4\right)dx  

 23 u2\frac{2}{3}\ u^2  

 01(x24x+4)dx+12x2dx\int_0^1\left(x^2-4x+4\right)dx+\int_1^2x^2dx  

 143 u2\frac{14}{3}\ u^2  

 12(x2(4x24x+4))dx\int_1^2\left(x^2-\left(4x^2-4x+4\right)\right)dx​  

6.

MULTIPLE SELECT QUESTION

30 sec • 1 pt

Media Image

SEÑALA TODAS LAS RESPUESTAS CORRECTAS:

Halla el área de la región del primer cuadrante limitada por las gráficas de f(x)=1xf\left(x\right)=\frac{1}{x}  ,  g(x)=1x2g\left(x\right)=\frac{1}{x^2}  y la recta  x=2x=2  .

 12(1x1x2)dx\int_1^2\left(\frac{1}{x}-\frac{1}{x^2}\right)dx  

 ln(2)12 u2\ln\left(2\right)-\frac{1}{2}\ u^2  

 02(1x1x2)dx\int_0^2\left(\frac{1}{x}-\frac{1}{x^2}\right)dx  

 143 u2\frac{14}{3}\ u^2  

 12(1x21x)dx\left|\int_1^2\left(\frac{1}{x^2}-\frac{1}{x}\right)dx\right|  

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Halla una primitiva F(x)F\left(x\right)  de la función  f(x)=8x3+2xf\left(x\right)=8x^3+2x  , que cumpla que  F(x)0   xRF\left(x\right)\ge0\ \ \ \forall x\in R  y de forma que el área comprendida entre la gráfica de  F(x)F\left(x\right)  , el eje de abscisas y las rectas  x=0x=0  y  x=1x=1   sea  4115\frac{41}{15}  .

 F(x)=2x4+x2+2F\left(x\right)=2x^4+x^2+2  

 F(x)=2x4+x2F\left(x\right)=2x^4+x^2  

 F(x)=2x4+x2+CF\left(x\right)=2x^4+x^2+C  

 F(x)=2x4+x2+4115F\left(x\right)=2x^4+x^2+\frac{41}{15}  

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