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3.4.2. The geometric meaning of the double integral

Lecture



Let an integrable function f ( x, y ) take in the domain D only positive values. Then the double integral 3.4.2. The geometric meaning of the double integral numerically equal to the volume of a vertical cylindrical body constructed on the basis of D and bounded above by a corresponding piece of the surface z = f ( x, y ).

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Lectures and tutorial on "Mathematical analysis. Integral calculus"

Terms: Mathematical analysis. Integral calculus

3.1.1. Definition of indefinite integral
3.1.2. Integral table. Definition and formulas
3.1.3. Integration task
3.2. The main methods of integration 3.2.1. Integration in parts
3.2.2. Replace integration variable
3.3. The definite integral and its applications 3.3.1. The concept of a definite integral
3.3.2. The geometric meaning of a definite integral
3.3.3. Newton-Leibniz formula
3.3.4. Area Calculation in Rectangular Coordinates
3.3.5. Calculating the arc length of a curve in rectangular coordinates
3.3.6. Calculation of the arc length of a curve defined in parametric form
3.3.7. Body volume of rotation
3.3.8. Improper integral
3.4. Multiple integrals and their applications 3.4.1. The concept of double integral
3.4.2. The geometric meaning of the double integral
3.4.3. Calculation of the double integral
3.4.4. Change the order of integration
3.4.5. Calculation of areas of flat figures
3.4.6. Double integral in polar coordinates
3.4.7. Calculation of the areas of flat figures in polar coordinates
3.4.8. Calculation of volumes using double integral
Examples of solving problems to the section integral calculus
Integrals. History reference. The use of integrals in practice