Quiz about DEFINITE INTEGRALS

Question 1

El valor de la integral $$\int_{-1}^1x^3dx$$ es:

Accepted Answer

Cero

Answer

Positivo

Answer

Negativo

Answer

No se puede determinar

Question 2

Al evaluar la integral

$$\int_0^{\pi}Cot^2\left(x\right)Tan\left(x\right)Sen\left(x\right)dx$$

Se tiene por resultado:

Accepted Answer

0

Answer

-1

Answer

$$\pi$$

Answer

Ninguna de las anteriores

Question 3

El valor de la integral definida $$\int_0^2x\sqrt[]{2x^2+1}dx$$ es:

Accepted Answer

$$\frac{13}{2}$$

Answer

$$\frac{18}{3}$$

Answer

$$\frac{27}{6}$$

Answer

$$\frac{28}{6}$$

Question 4

Al evaluar la integral

$$\int_1^4\sqrt{x}dx$$

se tiene por resultado:

Accepted Answer

$$\frac{14}{3}$$

Answer

$$\frac{2}{3}$$

Answer

0

Answer

Ninguna de las anteriores

Question 5

Resolver la siguiente integral

Accepted Answer

2.9975

Answer

3.5412

Answer

5.9310

Question 6

Question 6.

Accepted Answer

6.5

Answer

12/3

Answer

5.5

Answer

11/3

Question 7

Find the area under a curve defined by the equation 5x⁴+3x+7 between the x values 0 and 4.

Accepted Answer

1076

Answer

1200

Answer

1/12

Answer

1134

Question 8

For a function that is strictly decreasing, a right hand Riemann Sum is which of the following:

Accepted Answer

Underestimate

Answer

Overestimate

Answer

Exact Solution

Answer

Unable to Determine

Question 9

_{Evaluate the integral}

Accepted Answer

32/3

Answer

30/3

Answer

31/3

Answer

29/3

Question 10

Evaluate the definite integral.

Accepted Answer

9/2

Answer

3

Answer

9

Answer

Not possible

Question 11

Evaluate the definite integral.

Accepted Answer

20

Answer

40

Answer

10

Answer

Not possible

Question 12

Find the area under the curve y =3x²-2x from x= 1 to x =5.

Accepted Answer

100

Answer

99

Answer

150

Answer

152

Question 13

Based on the table, use a left Riemann sum and 4 sub-intervals to estimate the Area under the curve. (Choose the correct set-up.)

Accepted Answer

5(3) + 1(4) + 2(5) + 1(7)

Answer

5(4) + 1(5) + 2(7) + 1(6)

Answer

5(3) + 6(4) + 8(5) + 9(7)

Answer

0(3) + 5(4) + 6(5) + 8(7)

Question 14

Integrate the following indefinite integral via u-substitution $$\int_{ }^{ }\left(2+2x\right)e^{\left(4x+2x^2\right)}dx$$

Accepted Answer

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

Answer

$$2e^{\left(4x+2x^2\right)}+C$$

Answer

$$e^{2\left(4x+2x^2\right)}+C$$

Answer

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

Question 15

Evaluate the definite integral.
$$\int_0^2\ \frac{3x^2-1}{x^2}dx$$

Accepted Answer

$$\frac{13}{2}$$

Answer

$$\frac{12}{3}$$

Answer

$$\frac{11}{2}$$

Answer

$$\frac{11}{3}$$

Question 16

Question 16.

Accepted Answer

16/3

Answer

1/3

Answer

8/3

Answer

24/3

Question 17

Find the average value of the function $$f\left(x\right)=x+3$$ on the interval $$\left[3,9\right]$$

Accepted Answer

$$9$$

Answer

$$54$$

Answer

$$67.5$$

Answer

$$7.5$$

Question 18

The area under a curve is calculated using which mathematical concept?

Accepted Answer

definite integral

Answer

antiderivative

Answer

indefinite integral

Answer

derivative

Question 19

The result of $$\int_1^3\left(x-2\right)\ dx$$ is:

Accepted Answer

zero

Answer

positive

Answer

negative

Question 20

Question 20.

Accepted Answer

6.5

Answer

12/3

Answer

5.5

Answer

11/3

Question 21

Evaluate the definite integral.

Accepted Answer

9/2

Answer

3

Answer

9

Answer

Not possible

Question 22

Question 22.

Accepted Answer

-4

Answer

28

Answer

40

Answer

20

Question 23

Evaluate the definite integral.

Accepted Answer

8 pi

Answer

16 pi

Answer

128 pi

Answer

Not possible

Question 24

Question 24.

Accepted Answer

32

Answer

40

Answer

64

Answer

Not possible

Question 25

El valor de la integral $$\int_{-1}^1x^3dx$$ es:

Accepted Answer

Cero

Answer

Positivo

Answer

Negativo

Answer

No se puede determinar

Question 26

Una suma de Riemann que permite calcular la integral $$\int_1^2\left(3x^2-2x\right)dx$$ es:

Accepted Answer

$$\lim_{n\rightarrow\infty}\sum_{k=1}^{\infty}\left(\frac{1}{n}+4\ \frac{k}{n^2}+3\ \frac{k^{2\ }}{n^3}\right)$$

Answer

$$\lim_{n\rightarrow\infty}\sum_{k=1}^{\infty}\left(3\ \frac{k^2}{n^2}-2\ \frac{k}{n}\right)\ \frac{1}{n}$$

Answer

$$\lim_{n\rightarrow\infty}\sum_{k=1}^{\infty}\left(3\ \left(1+\frac{k}{n}\right)^2+2\ \left(1+\frac{k}{n}\right)\right)\ \frac{1}{n}$$

Answer

Ninguna de las anteriores

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