Exam 15: Multiple Integrals

Select the correct Answer for each question. -Evaluate the double integral by first identifying it as the volume of a solid.

Calculate the iterated integral.

Evaluate where and T is the region bounded by the paraboloid and the plane

Calculate the iterated integral.Round yourAnswer to two decimal places.

Use cylindrical or spherical coordinates, whichever seems more appropriate, to evaluate where E lies above the paraboloid and below the plane

Calculate the iterated integral.

Find the Jacobian of the transformation.

Use cylindrical coordinates to evaluate the triple integral where E is the solid that lies between the cylinders above the xy-plane and below the plane

Find the area of the surface S where S is the part of the sphere that lies to the right of the xz-plane and inside the cylinder

Determine whether to use polar coordinates or rectangular coordinates to evaluate the integral where is a continuous function.Then write an expression for the (iterated) integral.

An agricultural sprinkler distributes water in a circular pattern of radius ft.It supplies water to a depth of feet per hour at a distance of feet from the sprinkler.What is the total amount of water supplied per hour to the region inside the circle of radius feet centered at the sprinkler?

Evaluate the iterated integral by converting to polar coordinates.Round theAnswer to two decimal places.

Evaluate the triple integral.Round yourAnswer to one decimal place.

Evaluate the iterated integral.

Select the correct Answer for each question. -Use spherical coordinates.Evaluate here is the ball with center the origin and radius

The sketch of the solid is given below.Given write the inequalities that describe it.Select the correct Answer

Select the correct Answer for each question. -Find the center of mass of the lamina that occupies the region D and has the given density function, if D is bounded by the parabola and the x-axis.

The sketch of the solid is given below.Given , write the inequalities that describe it.

Select the correct Answer for each question. -Calculate the double integral.

Find the volume under and above the region bounded by and .