Exam 15: Multiple Integrals

Evaluate where is the figure bounded by

Use a triple integral to find the volume of the solid bounded by and the planes and Select the correct Answer

Describe the region whose area is given by the integral.

Calculate the double integral.

Use the Midpoint Rule with four squares of equal size to estimate the double integral.

Select the correct Answer for each question. -Use the given transformation to evaluate the integral. where R is the region in the first quadrant bounded by the lines and the hyperbolas

Find the mass and the center of mass of the lamina occupying the region R, where R is the triangular region with vertices and having the mass density Select the correct Answer

Use the given transformation to evaluate the integral. where R is the square with vertices (0, 0), (4, 6), (10, 2) and

Calculate the double integral.Select the correct Answer

Identify the surface with equation

Use polar coordinates to find the volume of the solid inside the cylinder and the ellipsoid

Find the area of the surface.The part of the surface that lies within the cylinder

Use cylindrical coordinates to evaluate Select the correct Answer

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

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

Select the correct Answer for each question. -The sketch of the solid is given below.Given , write the inequalities that describe it.

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

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

Select the correct Answer for each question. -Use the transformation to evaluate the integral here R is the region bounded by the ellipse