Exam 15: Multiple Integrals

Use polar coordinates to evaluate.

Calculate the iterated integral.

Use spherical coordinate to find the volume above the cone and inside sphere

Find the area of the part of the sphere that lies inside the paraboloid

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 Select the correct Answer

Use spherical coordinate to find the volume above the cone and inside sphere

Calculate the iterated integral.

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

Find the center of mass of the lamina of the region shown if the density of the circular lamina is four times that of the rectangular lamina.

Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse.Assume the vertex opposite the hypotenuse is located at and that the sides are along the positive axes.

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.

Calculate the iterated integral.

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

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

Use the given transformation to evaluate the integral. where R is the region in the first quadrant bounded by the lines and the hyperbolas

Evaluate the integral and with respect to n that order.Select the correct Answer

For which of the following regions would you use rectangular coordinates?

Use polar coordinates to find the volume of the sphere of radius Round to two decimal places.

Select the correct Answer for each question. -Use polar coordinates to find the volume of the solid under the paraboloid and above the disk

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