Search Header Logo

Triple integral

Authored by -- --

Mathematics

University

Used 42+ times

Triple integral
AI

AI Actions

Add similar questions

Adjust reading levels

Convert to real-world scenario

Translate activity

More...

    Content View

    Student View

5 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

E is the solid bounded by the paraboloid  y=x2+z2y=x^2+z^2 and  the plane  y=4  . Which of the following region is the projection of E on xy-plane ?

Media Image
Media Image
Media Image
Media Image

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A solid S is bounded by the planes  x+2y+z=2x+2y+z=2  , x=2yx=2y  , x=0x=0  and  z=0z=0  . View the solid S from xy-plane. Which of the following is NOT TRUE?

Upper surface:  z=2x2yz=2-x-2y  
Lower surface:  z=0z=0  

Upper surface:  z=2x2yz=2-x-2y  
Interval for y:  [0,x2]\left[0,\frac{x}{2}\right]  

Interval for x:  [0,1]\left[0,1\right]  
Interval for y:  [x2,1x2]\left[\frac{x}{2},1-\frac{x}{2}\right]  

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What   1 dV\int_{ }^{ }\int_{ }^{ }\int_{ }^{ }\ 1\ dV  stands for?

Area of region R

Volume of the solid

Mass of the solid

Height of the solid

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

 020z20(yz)(2xy)dxdydz\int_0^2\int_0^{z^2}\int_0^{\left(y-z\right)}\left(2x-y\right)dxdydz  =


 1415\frac{14}{15}  

 11  

 1315\frac{13}{15}  

 1615\frac{16}{15}  

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Media Image

The cone shape of a diamond earring has height = 2 cm and is placed at the origin of xyz axes as shown in the figure. If the density  f(x,y,z)=x2+y2f\left(x,y,z\right)=x^2+y^2  , set up the triple integral to find the mass of the cone.

 220101(x2+y2)dzdydx\int_{-2}^2\int_0^1\int_0^1\left(x^2+y^2\right)dzdydx  

 02π02r2r3dzdrdθ\int_0^{2\cdot\pi}\int_0^2\int_r^2r^3dzdrd\theta  

 02π02r22r2 dzdrdθ\int_0^{2\cdot\pi}\int_0^2\int_{r^2}^2r^2\ dzdrd\theta  

 ππ02r4r3 dzdrdθ\int_{-\pi}^{\pi}\int_0^2\int_r^4r^3\ dzdrd\theta  

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Google

Continue with Google

Email

Continue with Email

Classlink

Continue with Classlink

Clever

Continue with Clever

or continue with

Microsoft

Microsoft

Apple

Apple

Others

Others

Already have an account?