Exam 15: Multiple Integrals

Select the correct Answer for each question. -A swimming pool is circular with a diameter.The depth is constant along east-west lines and increases linearly from ft at the south end to ft at the north end.Find the volume of water in the pool.

Select the correct Answer for each question. -Evaluate the iterated integral.

Calculate the iterated integral.

Find the area of the surface.The part of the surface that lies above the xy-plane.

Use cylindrical coordinates to evaluate

Use the transformation to evaluate the integral where R is the region bounded by the ellipse

Sketch the solid whose volume is given by the iterated integral

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

Evaluate the iterated integral.Select the correct Answer

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

Select the correct Answer for each question. -Evaluate the iterated integral by converting to polar coordinates.Round theAnswer to two decimal places.

Find the mass of the lamina that occupies the region and has the given density function.Round yourAnswer to two decimal places.

Sketch the solid bounded by the graphs of the equations and and then use a triple integral to find the volume of the solid.

Select the correct Answer for each question. -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 center of mass of a homogeneous solid bounded by the paraboloid and

An electric charge is spread over a rectangular region Find the total charge on R if the charge density at a point in R (measured in coulombs per square meter) is Select the correct Answer

Find the Jacobian of the transformation.

Find the volume of the solid bounded by the surface and the planes and coordinate planes.Select the correct Answer

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

Select the correct Answer for each question. -Use the Midpoint Rule with four squares of equal size to estimate the double integral.