ИДЗ 13.1 – Вариант 18. 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.

1.18. D: y = √4 - x2, x ≥ 0, x = 1, y = 0.

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

 D: y2 = 1 - x, x ≥ 0

3. Calculate the double integral using polar coordinates.

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

4.18. D: y = -2x2 + 2, y ≥ - 6.

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

5.18. (X2 + y2) 3 = a2x4

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

6.18. x2 = 1 - y, x + y + z = 3, y ≥ 0, z ≥ 0

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