Exam 15: Multiple Integrals

Select the correct Answer for each question. -Use a triple integral to find the volume of the solid bounded by and the planes and

Select the correct Answer for each question. -Use cylindrical coordinates to evaluate where T is the solid bounded by the cylinder and the planes and

Find the area of the part of the sphere that lies inside the paraboloid Select the correct Answer

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.

Use a computer algebra system to find the moment of inertia of the lamina that occupies the region D and has the density function

Use a double integral to find the area of the region R where R is bounded by the circle

Use cylindrical coordinates to evaluate where E is the region that lies inside the cylinder and between the planes Round theAnswer to two decimal places.

Evaluate the integral by making an appropriate change of variables.Round yourAnswer to two decimal places. R is the parallelogram bounded by the lines

Find the mass of the lamina that occupies the region D and has the given density function, if D is bounded by the parabola and the line

Find the mass and the center of mass of the lamina occupying the region R, where R is the region bounded by the graphs of and having the mass density

Find the area of the surface S where S is the part of the plane that lies above the triangular region with vertices

Find the area of the surface S where S is the part of the sphere that lies inside the cylinder

Find the area of the surface.Round yourAnswer to three decimal places.

Find the mass of the lamina that occupies the region D and has the given density function, if D is bounded by the parabola and the line Select the correct Answer

Evaluate the integral by changing to polar coordinates. is the region bounded by the semicircle and the -axis.

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

Use cylindrical coordinates to evaluate where E is the region that lies inside the cylinder and between the planes Round theAnswer to two decimal places.

Find the mass of the solid S bounded by the paraboloid and the plane if S has constant density 3.Select the correct Answer

Find the area of the part of hyperbolic paraboloid that lies between the cylinders