Triple Integrals (Rectangular) Practice

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

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

What does  $$\int_{ }^{ }\int_{ }^{ }\int_{ }^{ }\ 1\ dV$$  mean?

$$\int_0^2\int_0^{z^2}\int_0^{\left(y-z\right)}\left(2x-y\right)dxdydz$$  =

Find the upper limit of z in the triple integral

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 $$dzdydx$$  .

Find the upper limit of y in the triple integral

Find the volume of the solid D (leave your answer correct to two decimal places) in the triple integral

(a)  

Find the volume of the solid in the first octant enclosed by $$z=y,\ y^2=x,\ x=1$$  

(a)  

The object shown has a density given by $$2x$$  . What is the weight of the object?

(a)