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3.4.3. Calculation of the double integral

Lecture



If the boundary of the region D is intersected by any straight line x = c ( c - const ) at no more than two points, then the domain D is called regular in the direction of the axis OX . The bounded domain D , correct in the direction of the OX axis, is given by the inequalities:

a ≤ x ≤ b , φ 1 ( x ) ≤ yφ 2 ( x ) ,

where φ 1 ( x ) , φ 2 ( x ) are functions that are continuous on the interval [ a, b ] .

In this case, the double integral reduces to a double integral   3.4.3.  Calculation of the double integral .
First, assuming that the integration variable x is constant, we find a definite integral   3.4.3.  Calculation of the double integral as a function of f ( x ) variable x .
Then we find a definite integral   3.4.3.  Calculation of the double integral .


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Mathematical analysis. Integral calculus

Terms: Mathematical analysis. Integral calculus