# Calculus Early Transcendentals

Mathematics

## Quiz 12 :Multiple Integrals

Question Type
Find the center of mass of a homogeneous solid bounded by the paraboloid and
Free

Tags
Choose question tag
Use cylindrical or spherical coordinates, whichever seems more appropriate, to evaluate where E lies above the paraboloid and below the plane .
Free
Multiple Choice

E

Tags
Choose question tag
Use the transformation to evaluate the integral , where R is the region bounded by the ellipse .
Free
Multiple Choice

C

Tags
Choose question tag
Find the mass of the solid S bounded by the paraboloid and the plane if S has constant density 3.
Multiple Choice
Tags
Choose question tag
Find the Jacobian of the transformation.
Tags
Choose question tag
Use cylindrical coordinates to evaluate the triple integral where E is the solid that lies between the cylinders and above the xy-plane and below the plane .
Multiple Choice
Tags
Choose question tag
Use a triple integral to find the volume of the solid bounded by and the planes and .
Multiple Choice
Tags
Choose question tag
Find the Jacobian of the transformation.
Multiple Choice
Tags
Choose question tag
Use the given transformation to evaluate the integral. , where R is the region in the first quadrant bounded by the lines and the hyperbolas .
Multiple Choice
Tags
Choose question tag
Identify the surface with equation
Tags
Choose question tag
Identify the surface with equation
Tags
Choose question tag
Use cylindrical coordinates to evaluate where T is the solid bounded by the cylinder and the planes and
Multiple Choice
Tags
Choose question tag
Find the mass of a solid hemisphere of radius 5 if the mass density at any point on the solid is directly proportional to its distance from the base of the solid.
Multiple Choice
Tags
Choose question tag
Evaluate the integral by making an appropriate change of variables. Round your answer to two decimal places. R is the parallelogram bounded by the lines .
Tags
Choose question tag
Calculate the iterated integral.
Multiple Choice
Tags
Choose question tag
Use spherical coordinates to find the volume of the solid that lies within the sphere above the xy-plane and below the cone . Round the answer to two decimal places.
Tags
Choose question tag
Use the given transformation to evaluate the integral. , where R is the square with vertices (0, 0), (4, 6), (6, ), (10, 2) and
Multiple Choice
Tags
Choose question tag
Use spherical coordinates to find the moment of inertia of the solid homogeneous hemisphere of radius and density 1 about a diameter of its base.
Multiple Choice