Quiz about Repaso Cálculo Integral - 2023A

Question 1

Determinar la diferencial de $$y=\frac{(2x-3)}{(4x+5)}$$

Accepted Answer

$$dy=\frac{22}{(4x+5)^2dx}$$

Answer

$$dy=\frac{15}{(4x+5)^2dx}$$

Answer

$$dy=\frac{20}{(4x+5)^2dx}$$

Answer

$$dy=\frac{24}{(4x+5)^2dx}$$

Question 2

Determinar la diferencial de $$y=5x^3-6x^2+7x-5$$

Accepted Answer

$$dy=(15x^2-12x+7)dx$$

Answer

$$dy=(15x^3-12x^2+7x)dx$$

Answer

$$dy=(8x^2-8x+7)dx$$

Answer

$$dy=(15x^2+12x+7)dx$$

Question 3

$$Calcular\ el\ valor\ aproximado\ de\ ∛210\ si\ ∛125=5$$

Accepted Answer

6.1333

Answer

6.1111

Answer

6.1777

Answer

6.1555

Question 4

$$Calcular\ el\ valor\ aproximado\ de\ ∛50\ si\ ∛64=4$$

Accepted Answer

3.708

Answer

4.225

Answer

4.175

Answer

3.506

Question 5

$$Calcular\ el\ valor\ aproximado\ de\ \ \sqrt[]{115},\ si\ \ \sqrt[]{121\ }=11$$

Accepted Answer

10.72727273

Answer

10.73737374

Answer

10.74747475

Answer

10.75757576

Question 6

Hallar la integral de $$\int(36x^3-15x^2-16x+12)dx$$

Accepted Answer

$$9x^4-5x^3-8x^2+12x+C$$

Answer

$$4x^4-3x^3-6x^2-12x+C$$

Answer

$$10x^4-30x^3-8x^2+18x+C$$

Answer

$$48x^4-6x^3-9x^2+12x+C$$

Question 7

Determina la integral de $$\int\left(4x^2-9)^9(10xdx\right)$$

Accepted Answer

$$\frac{(4x^2-9)^{10}}{8}+C$$

Answer

$$\frac{(4x^2-9)^{10}}{10}+C$$

Answer

$$\frac{(4x^2-9)^{10}}{9}+C$$

Answer

$$\frac{(4x^2-9)^{10}}{6}+C$$

Question 8

Determina la integral de $$\int(10x^3-9)^5(40x^2dx)$$

Accepted Answer

$$\frac{2(10x^3-9)^6}{9}+C$$

Answer

$$\frac{2(10x^3-9)^6}{7}+C$$

Answer

$$\frac{4(10x^3-9)^6}{9}+C$$

Answer

$$\frac{4(10x^3-9)^6}{7}+C$$

Question 9

Determina la integral de $$\int∛((12x^4-7)^4)(8x^3dx)$$

Accepted Answer

$$\frac{\sqrt[3]{(12x^4-7)^7}}{14}+C$$

Answer

$$\frac{\sqrt[3]{(12x^4-7)^7}}{7}+C$$

Answer

$$\frac{\sqrt[3]{(12x^4-7)^7}}{12}+C$$

Answer

$$\frac{\sqrt[3]{(12x^4-7)^7}}{21}+C$$

Question 10

Es el resultado de integrar $$\int6x^3e^{x^4})dx$$

Accepted Answer

$$\frac{3}{2}e^{x^4}+C$$

Answer

$$\frac{1}{3}e^{x^4}+C$$

Answer

$$\frac{1}{2}e^{x^4}+C$$

Answer

$$\frac{2}{3}e^{x^4}+C$$

Question 11

Es el resultado de integrar $$\int e^{ax^2}\left(2x\ dx\right)$$

Accepted Answer

$$\frac{1}{a}e^{ax^2}+C$$

Answer

$$ae^{ax^2}+C$$

Answer

$$a^{\frac{1}{2}e^{ax^2}}+C$$

Answer

$$a^2\ e^{ax^2}+C$$

Question 12

Es el resultado de integrar $$\int e^{\frac{1}{2}x^2}(xdx)$$

Accepted Answer

$$e^{\frac{1}{2}x^2}+C$$

Answer

$$2e^{\frac{1}{2}x^2}+C$$

Answer

$$\frac{1}{2}e^{\frac{1}{2}x^2}+C$$

Answer

$$2xe^{\frac{1}{2}x^2}+C$$

Question 13

UTILIZA EL METODO DE FRACCIONES PARCIALES PARA OBTENER EL RESULTADO DE $$\ \ \int\frac{dx}{x^2-9x}$$

Accepted Answer

$$\frac{1}{9}\ln|\frac{x-9}{x}|+C$$

Answer

$$9\ln|\frac{x}{x-9}|+C$$

Answer

$$\frac{1}{9}\ln|\frac{x}{x-9}|+C$$

Answer

$$9\ln|\frac{x-9}{x}|+C$$

Question 14

UTILIZA EL METODO DE FRACCIONES PARCIALES PARA OBTENER EL RESULTADO DE: $$\int\ \frac{dx}{x^2-7x+12}$$

Accepted Answer

$$\ln|\frac{x-4}{x-3}|+C$$

Answer

$$\frac{1}{2}\ln|\frac{x-4}{x-3}|+C$$

Answer

$$\frac{1}{2}\ln|\frac{x-3}{\ x-4}|+C$$

Answer

$$\ln|\frac{x-3}{\ x-4}|+C$$

Question 15

UTILIZA EL METODO DE FRACCIONES PARCIALES PARA OBTENER EL RESULTADO DE: $$\int\ \frac{dx}{x^2-49}$$

Accepted Answer

$$\frac{1}{14}\ln|\frac{x-7}{x+7}|+C$$

Answer

$$\frac{1}{14}\ln|\frac{x+7}{x-7}|+C$$

Answer

$$14\ln|\frac{x+7}{x-7}|+C$$

Answer

$$14\ln|\frac{x-7}{x+7}|+C$$

Question 16

CALCULA LA INTEGRAL DEFINIDA: $$\int_1^2(2x+1)^3dx$$

Accepted Answer

$$68$$

Answer

$$58$$

Answer

$$78$$

Answer

$$48$$

Question 17

CALCULA LA INTEGRAL DEFINIDA: $$\int_2^82dx$$

Accepted Answer

12

Answer

17

Answer

16

Answer

18

Question 18

CALCULA LA INTEGRAL DEFINIDA: $$\int_2^5(3x^2-8x)dx$$

Accepted Answer

33

Answer

36

Answer

30

Answer

39

Question 19

CALCULA LA INTEGRAL DEFINIDA: $$\int_2^5\ 3\sqrt{(}x-1)dx$$

Accepted Answer

14

Answer

12

Answer

18

Answer

16

Question 20

CALCULA LA INTEGRAL DEFINIDA: $$\int_0^{\pi/2}\ \cos x\ dx$$

Accepted Answer

1

Answer

-1

Answer

2

Answer

-2

Question 21

CALCULA LA INTEGRAL DEFINIDA: $$\int_{\pi/3}^{\pi/2}\ senx\ dx$$

Accepted Answer

$$-\frac{1}{2}$$

Answer

$$-\frac{1}{3}$$

Answer

$$\frac{1}{3}$$

Answer

$$\frac{1}{2}$$

Question 22

CALCULA LA INTEGRAL DEFINIDA: $$\int_2^6\ \frac{dx}{x}$$

Accepted Answer

$$\ln⁡3$$

Answer

$$\ln⁡4$$

Answer

$$\ln⁡6$$

Answer

$$\ln⁡5$$

Question 23

CALCULA LA INTEGRAL DEFINIDA: $$\int_e^{2e}\ \frac{3dx}{x}$$

Accepted Answer

2.079

Answer

2.089

Answer

2.069

Answer

2.099

Question 24

CALCULA LA INTEGRAL DEFINIDA: $$\int_1^9\ \frac{dx}{x+3}$$

Accepted Answer

$$\ln⁡3$$

Answer

$$\ln⁡6$$

Answer

$$\ln⁡4$$

Answer

$$\ln⁡2$$

Question 25

CALCULA LA INTEGRAL DEFINIDA: $$\int_2^4\ (3x^2-6x+5)dx$$

Accepted Answer

30

Answer

34

Answer

32

Answer

28

Question 26

CALCULA LA INTEGRAL DEFINIDA: $$\int_1^3\ (6-4x)dx$$

Accepted Answer

-4

Answer

-2

Answer

-1

Answer

-3

Question 27

CALCULA LA INTEGRAL DEFINIDA: $$\int_1^3\ (3x^2-6x)dx$$

Accepted Answer

$$2u^2\ \ $$

Answer

$$3u^2$$

Answer

$$\ \ 6u^2\ \ $$

Answer

$$4u^2$$

Question 28

CALCULA LA INTEGRAL DEFINIDA: $$\int_{-1}^3\ (x-1)^2dx$$

Accepted Answer

$$\frac{16}{3}u^2\ $$

Answer

$$\frac{11}{3}u^2\ \ $$

Answer

$$\frac{14}{3}u^2\ \ $$

Answer

$$\frac{17}{3}u^2$$

Question 29

CALCULA LA INTEGRAL DEFINIDA: $$\int_0^2\ x^2dx$$

Accepted Answer

$$\frac{8}{3}u^2\ \ $$

Answer

$$\frac{4}{3}u^2\ \ $$

Answer

$$\frac{7}{3}u^2\ \ $$

Answer

$$\frac{5}{3}u^2$$

Question 30

Determina la integral de: $$\int_{ }^{ }\left(4^{x^4}-9\right)\left(36^{x^3}\ dx\right)$$

Accepted Answer

$$\frac{9\left(4^{x^4}-9\right)^8}{32}+C$$

Answer

$$\frac{7\left(4^{x^4}-9\right)^8}{32}+C$$

Answer

$$\frac{11\left(4^{x^4}-9\right)^8}{32}+C$$

Answer

$$\frac{13\left(4^{x^4}-9\right)^8}{32}+C$$

Question 31

Determina la integral de: $$\int_{ }^{ }\ \frac{20x^3\ dx}{\left(20x^4-9\right)^3}$$

Accepted Answer

$$-\frac{1}{4\left(20x^4-9\right)^2}+C$$

Answer

$$-\frac{1}{2\left(20x^4-9\right)^2}+C$$

Answer

$$-\frac{1}{8\left(20x^4-9\right)^2}+C$$

Answer

$$-\frac{1}{6\left(20x^4-9\right)^2}+C$$

Question 32

Determina la integral de: $$\int_{ }^{ }\ 8x^3\ \csc\ \left(6x^4\right)\cot\ \left(6x^4\right)\ dx$$

Accepted Answer

$$-\frac{1}{3}\csc\left(6x^4\right)+C$$

Answer

$$-6\csc\left(6x^4\right)+C$$

Answer

$$-3\csc\left(6x^4\right)+C$$

Answer

$$-\frac{1}{6}\csc\left(6x^4\right)+C$$

Question 33

Hallar la integral de: $$\int_{ }^{ }\ 20x^4\ \cot\ \left(12x^5\right)dx$$

Accepted Answer

$$\frac{1}{3}Ln\ \left|sen\ 12x^5\right|+C$$

Answer

$$\frac{1}{6}Ln\ \left|sen\ 12x^5\right|+C$$

Answer

$$\frac{1}{4}Ln\ \left|sen\ 12x^5\right|+C$$

Answer

$$\frac{1}{8}Ln\ \left|sen\ 12x^5\right|+C$$

Question 34

Halla la integral de: $$\int_{ }^{ }\ \left(Sec\left(4x^2\right)Tan\left(4x^2\right)\right)\left(4x\ dx\right)$$

Accepted Answer

$$\frac{1}{2}\ Sec\left(4x^2\right)+C$$

Answer

$$2\ Sec\left(4x^2\right)+C$$

Answer

$$\frac{1}{4}\ Sec\left(4x^2\right)+C$$

Answer

$$4\ Sec\left(4x^2\right)+C$$

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