ИДЗ 13.1 – Вариант 15. Решения Рябушко А.П.

1. Provide a double integral as an iterated integral with the outer integration over x and external integration with respect to y, if D is given the above lines.

1.15. D: y = 0, y ≥ x, y = -√2 - x2.

2. Calculate the double integral over the region D, limited to lines.

 D: y = x3, y = 8, y = 0, x = 3

3. Calculate the double integral using polar coordinates.

4. Calculate the area of a plane region D, bounded set tench.

4.15. D: y = x2 + 4x, y = x + 4

5. Use double integrals in polar coordinates to calculate the flat area of the figure bounded by the lines indicated.

5.15. (X2 + y2) 3 = a4x2

6. Calculate the volume of the body bounded by a given surface.

6.15. 3y = √x, y ≤ x, x + y + z = 10, y = 1, z = 0

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