Lecture
Let a double integral be given . If the integration domain is D (Fig. 15), given by the inequalities is also correct with respect to the OS axis, i.e. the boundary of the domain D is intersected by the straight line y = c ( c constant) at no more than two points, then the domain D can be given by other inequalities:
.
Here α and β are the largest and smallest values of y in the domain D , respectively;
x = 1 ( y ) is the left side of the boundary;
x = ψ 2 ( y ) is the right side of the boundary of the domain D.
Then in the double integral you can change the order of integration:
Fig. 15
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Mathematical analysis. Integral calculus
Terms: Mathematical analysis. Integral calculus