Exam 12: Extension D: Multiple Integrals

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

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

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.

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

A lamina occupies the part of the disk in the first quadrant.Find its center of mass if the density at any point is proportional to its distance from the x-axis.