Instruction

1

The solution of the double integrals can be reduced to the computation of definite integrals.

If the function f(x, y) is a closed and continuous in a region D bounded by the line y = c and the line x = d, with c < d and a function y = g(x) and y = z(x), with g(x), z(x) is continuous on [c; d] and g(x) ? z(x) on this interval, then calculate the double integral by the formula presented in the figure.

If the function f(x, y) is a closed and continuous in a region D bounded by the line y = c and the line x = d, with c < d and a function y = g(x) and y = z(x), with g(x), z(x) is continuous on [c; d] and g(x) ? z(x) on this interval, then calculate the double integral by the formula presented in the figure.

2

If the function f(x, y) is a closed and continuous in a region D bounded by the line y = c and the line x = d, with c < d and a function y = g(x) and y = z(x), with g(x), z(x) is continuous on [c; d] and g(x) = z(x) on this interval, then calculate the double integral by the formula presented in the figure.

3

If you want to calculate the double integral more complex regions D, the region D is split into parts, each of which represents an area described in paragraph 1 or 2. Calculates the integral for each of these areas, the results obtained are summarized.