Quiz about untitled

Question 1

$$\int\int\int\left(2x-3y+4z\right)dxdydz$$

Accepted Answer

$$xyz\left(x-\frac{3}{2}y+2z\right)+C$$

Answer

$$xyz\left(x+\frac{3}{2}y+2z\right)+C$$

Answer

$$xyz\left(x-3y+2z\right)+C$$

Answer

$$xyz\left(x+3y+2z\right)+C$$

Question 2

$$\int\int\int\left(x^2+y^2+z^2\right)dxdydz$$

Accepted Answer

$$\frac{1}{3}xyz\left(x^2+y^2+z^2\right)+C$$

Answer

$$3xyz\left(x^2yz+xy^2z+xyz^2\right)+C$$

Answer

$$xyz\left(x^2yz+xy^2z+xyz^2\right)+C$$

Answer

$$\frac{1}{3}xyz\left(x^2y^2z+xy^2z^2+x^2yz^2\right)+C$$

Question 3

$$\int\int\int e^{4x}dxdydz$$

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 4

$$\int_0^1\int_1^2\int_3^4\ \left(-x-y-z\right)dxdydz$$

Accepted Answer

-5.50

Answer

5.50

Answer

8.50

Answer

-8.50

Question 5

$$\int_2^4\int_6^8\int_{-2}^{-4}\ \cos\left(y\right)\ dxdydz$$

Accepted Answer

$$\approx-5.08$$

Answer

$$-8.05$$

Answer

$$\approx-0.192$$

Answer

$$\approx-2.19$$

Question 6

$$\int_2^4\int_6^8\int_{-2}^{-4}\ \left(e^z\right)\ dxdydz$$

Accepted Answer

$$\approx-189$$

Answer

$$\approx-132$$

Answer

$$\approx538$$

Answer

$$\approx710$$

Question 7

Find the lower limit of z in the triple integral

$$\int_{ }^{ }\int_{ }^{ }\int_D^{ }\ \ f\left(x,y,z\right)dV$$ if D is the solid bounded by $$z=4-y,\ z=y-6$$ and $$y=x^2,$$ taking the order of integration as $$dzdydx$$ .

Accepted Answer

$$y-6$$

Answer

$$5$$

Answer

$$4-y$$

Answer

$$0$$

Question 8

Find the upper limit of z in the triple integral

$$\int_{ }^{ }\int_{ }^{ }\int_D^{ }\ \ f\left(x,y,z\right)dV$$ if D is the solid bounded by $$z=4-y,\ z=y-6\ $$ and $$y=x^2,$$ taking the order of integration as $$dzdydx$$ .

Accepted Answer

$$4-y$$

Answer

$$5$$

Answer

$$y-6$$

Answer

$$0$$

Question 9

Find the upper limit of y in the triple integral

$$\int_{ }^{ }\int_{ }^{ }\int_D^{ }\ \ f\left(x,y,z\right)dV$$ if D is the solid bounded by $$z=4-y,\ z=y-6$$ and $$y=x^2,$$ taking the order of integration as $$dzdydx$$ .

Accepted Answer

$$5$$

Answer

$$x^2$$

Answer

$$z+6$$

Answer

$$0$$

Question 10

$$\int\int\int\left(2x-3y+4z\right)dxdydz$$

Accepted Answer

$$xyz\left(x-\frac{3}{2}y+2z\right)+C$$

Answer

$$xyz\left(x+\frac{3}{2}y+2z\right)+C$$

Answer

$$xyz\left(x-3y+2z\right)+C$$

Answer

$$xyz\left(x+3y+2z\right)+C$$

Question 11

$$\int\int\int\left(x^2+y^2+z^2\right)dxdydz$$

Accepted Answer

$$\frac{1}{3}xyz\left(x^2+y^2+z^2\right)+C$$

Answer

$$3xyz\left(x^2yz+xy^2z+xyz^2\right)+C$$

Answer

$$xyz\left(x^2yz+xy^2z+xyz^2\right)+C$$

Answer

$$\frac{1}{3}xyz\left(x^2y^2z+xy^2z^2+x^2yz^2\right)+C$$

Question 12

$$\int\int\int e^{4x}dxdydz$$

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 13

$$\int_0^1\int_1^2\int_3^4\ \left(-x-y-z\right)dxdydz$$

Accepted Answer

-5.50

Answer

5.50

Answer

8.50

Answer

-8.50

Question 14

$$\int_2^4\int_6^8\int_{-2}^{-4}\ \cos\left(y\right)\ dxdydz$$

Accepted Answer

$$\approx-5.08$$

Answer

$$-8.05$$

Answer

$$\approx-0.192$$

Answer

$$\approx-2.19$$

Question 15

$$\int_2^4\int_6^8\int_{-2}^{-4}\ \left(e^z\right)\ dxdydz$$

Accepted Answer

$$\approx-189$$

Answer

$$\approx-132$$

Answer

$$\approx538$$

Answer

$$\approx710$$

Question 16

Determine the intervals for $$r$$ and $$ heta$$ associated with the blue region.

Accepted Answer

$$2\le r\le4,\ \frac{\pi}{4}\le heta\le\pi$$

Answer

$$3\le r\le4,\ 0\le heta\le\pi$$

Answer

$$2\le r\le4,\ 0\le heta\le\frac{\pi}{4}$$

Answer

$$\pi\le r\le\frac{\pi}{4},\ 1\le heta\le4$$

Question 17

Convert $$\int_0^{\frac{1}{\sqrt{2}}}\int_x^{\sqrt{1-x^2}}\left(3x\ +4y^2\right)\ dydx$$ into polar coordinates

Accepted Answer

$$\int_{\frac{\pi}{4}}^{\frac{\pi}{2}}\int_0^1r^2\left(3\cos heta+4r\sin^2 heta ight)drd heta$$

Answer

$$\int_0^{\frac{\pi}{4}}\int_0^13r+4r\sin heta\ drd heta$$

Answer

$$\int_0^{\frac{\pi}{2}}\int_0^13r\cos heta+4r^2\sin^2 heta\ drd heta$$

Answer

$$\int_{\frac{\pi}{3}}^{\frac{\pi}{2}}\int_0^13\cos heta+4r^2\sin^2 heta\ r\ drd heta$$

Question 18

Set up limit of triple integral to find the volume of the solid that lies below the hemisphere $$z=\sqrt{25-x^2-y^2}$$ between cylinder $$x^2+y^2=16$$ and $$x^2+y^2=25$$ using cylindrical coordinates.

Accepted Answer

$$\int_0^{2\pi}\int_4^5\int_0^{\sqrt{25-r^2}}rdzdrd heta$$

Answer

$$\int_0^{2\pi}\int_0^4\int_0^{\sqrt{25-r^2}}rdzdrd heta$$

Answer

$$\int_0^{2\pi}\int_0^5\int_0^{\sqrt{25-r^2}}rdzdrd heta$$

Answer

$$\int_0^{2\pi}\int_4^5\int_0^5rdzdrd heta$$

Question 19

In $$\int_0^1\int_0^{1-z}\int_0^{1-y-z}xyzdxdydz$$ the limit of x varies from____________

Accepted Answer

0 to 1-y-z

Answer

0 to 1

Answer

0 to 1-z

Answer

1 to 1-y-z

Question 20

Determine the intervals for $$r$$ and $$ heta$$ associated with the blue region.

Accepted Answer

$$2\le r\le4,\ \frac{\pi}{4}\le heta\le\pi$$

Answer

$$3\le r\le4,\ 0\le heta\le\pi$$

Answer

$$2\le r\le4,\ 0\le heta\le\frac{\pi}{4}$$

Answer

$$\pi\le r\le\frac{\pi}{4},\ 1\le heta\le4$$

Question 21

$$\int_0^{\pi/2}\int_0^{\pi/2}\cos heta\cos\varphi d heta d\varphi$$ is ___________

Accepted Answer

1

Answer

0

Answer

$$\pi$$

Answer

$$\frac{\pi}{2}$$

Question 22

$$\int_1^2\int_0^2e^xdydx$$ is ___________

Accepted Answer

$$2\left(e^2-e\right)$$

Answer

$$e^2-e$$

Answer

$$e^2$$

Answer

$$e^2-1$$

Question 23

Set up limit of triple integral to find the volume of the solid that lies below the hemisphere $$z=\sqrt{25-x^2-y^2}$$ between cylinder $$x^2+y^2=16$$ and $$x^2+y^2=25$$ using cylindrical coordinates.

Accepted Answer

$$\int_0^{2\pi}\int_4^5\int_0^{\sqrt{25-r^2}}rdzdrd heta$$

Answer

$$\int_0^{2\pi}\int_0^4\int_0^{\sqrt{25-r^2}}rdzdrd heta$$

Answer

$$\int_0^{2\pi}\int_0^5\int_0^{\sqrt{25-r^2}}rdzdrd heta$$

Answer

$$\int_0^{2\pi}\int_4^5\int_0^5rdzdrd heta$$

Question 24

$$\int_0^2\int_0^{\infty}e^{-x}dxdy$$ is ___________

Accepted Answer

2

Answer

1

Answer

$$e^2-1$$

Answer

$$e^{-2}-1$$

Question 25

$$\int_1^2\int_0^2e^xdydx$$ is ___________

Accepted Answer

$$2\left(e^2-e\right)$$

Answer

$$e^2-e$$

Answer

$$e^2$$

Answer

$$e^2-1$$

Question 26

$$\int_0^2\int_0^yx^2dxdy$$ is ___________

Accepted Answer

$$\frac{4}{3}$$

Answer

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

Answer

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

Answer

$$\frac{5}{3}$$

Question 27

Calculate the value of the multiple integral $$\int_{ }^{ }\int_D^{ }\left(x^2+y^2\right)^{\frac{3}{2}}dA$$ , where $$D$$ is the region in the first quadrant bounded by the lines $$y=0$$ and $$y=\sqrt[]{3}x$$ and the circle $$x^2+y^2=9$$ . The result is equal to___

Accepted Answer

$$\frac{81\pi}{5}$$

Answer

$$\frac{27\pi}{5}$$

Answer

$$\frac{9\pi}{5}$$

Answer

$$\frac{3\pi}{5}$$

Question 28

Is it TRUE or FALSE:

$$\int_{-1}^2\int_0^5x^2\sin\left(x-y\right)dxdy=\int_0^5\int_{-1}^2x^2\sin\left(x-y\right)dydx$$

Accepted Answer

TRUE

Answer

FALSE

Question 29

What is the concept of iterated integrals?

Accepted Answer

A mathematical concept used to calculate multiple integrals by breaking the region into smaller pieces and integrating over each piece.

Answer

A cooking technique used to prepare multiple dishes simultaneously

Answer

A concept in computer programming for repeating a sequence of instructions

Answer

A method for solving algebraic equations using repeated addition

Question 30

How do you determine the limits of integration for a double integral?

Accepted Answer

Consider the region of integration and the bounds of the variables involved.

Answer

Guess randomly

Answer

Use the value of the function at a single point

Answer

Ask someone else to determine the limits

Question 31

Determine el valor de la integral que se muestra en la imagen

Accepted Answer

200

Answer

49

Answer

15

Answer

175

Question 32

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

Accepted Answer

Cero

Answer

Positivo

Answer

Negativo

Answer

No se puede determinar

Question 33

Question 33.

Accepted Answer

$$10.5$$

Answer

$$21$$

Answer

$$11$$

Answer

$$12.5$$

Question 34

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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