Advanced Calculus fi..

Chapter 4 Integral Calculus of Functions of Several Variables 229111. Mass. If f is interpreted as density, that is, as mass per unit area, thenM = mass of R = (4.37)IV. Center ofmass. If f is density, then the center of mass (2, J) of the thin platerepresented by R is located by the equationsRwhere M is given by (4.37).V. Moment of inertia. The moments of inertia of the thin plate about the x- andy-axes are given by the equationswhile the polar moment of inertia about the origin 0 is given byThe basic properties of the double integral are essentially the same as those forthe definite integral:where R is composed of two pieces R1 and R2 overlapping only at boundary points;where A is the area of R, as in (4.36), and (x,, y,) is a suitably chosen point of R;