From a course of the mathematical analysis the concept of double integral is known. Geometrically double integral represents the volume of a cylindrical body on the basis of D and z limited to a surface = f (x, y). By means of double integrals it is possible to calculate the mass of a thin plate with the set density, the area of a flat figure, the area of a piece of a surface, coordinate of the center of gravity of a uniform plate and other sizes.
Instruction
1. The solution of double integrals can be consolidated to calculation of certain integrals. If function f (x, y) d is closed and continuous in some area D, limited line y = c and line x =, at this c <d and also functions y = g(x) and y = z(x), at this g(x), z(x) – are continuous on [c; d] and g (x)? z(x) on this piece, it is possible to calculate double integral on the formula presented in the drawing.
2. If function f (x, y) d is closed and continuous in some area D, limited line y = c and line x =, at this c <d and also functions y = g(x) and y = z(x), at this g(x), z(x) – are continuous on [c; d] and g(x) = z(x) on this piece, it is possible to calculate double integral on the formula presented in the drawing.
3. If it is necessary to calculate double integral on more difficult areas D, then area D is segmented, each of which represents the area presented in Paragraph 1 or 2. The integral each of these areas is expected, the received results are summarized.