ИДЗ 13.1 – Вариант 19. 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.

1.19. D: x = -1, x = -2, y ≥ 0, y = x2

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

 D: y = x + 5, x + y + 5 = 0, x ≤ 0

3. Calculate the double integral using polar coordinates.

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

4.19. D: y2 = 4x, x = 8 / (y2 + 4)

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

5.19. (X2 + y2) 2 = 4 (3x2 + 4y2)

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

6.19. x = y2, x = 1, x + y + z = 4, z = 0

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