ИДЗ 13.1 – Вариант 5. 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.

1.5. D: x2 = 2 - y, x + y = 0

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

 D: y = x2 - 1, x ≥ 0, y ≤ 0

3. Calculate the double integral using polar coordinates.

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

4.5. D: y = 8 / (x2 + 4), x2 = 4y.

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

5.5. x4 - y4 = (x2 + y2) 3

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

6.5. z = 2x2 + y2, y ≤ x, y = 3x, x = 2, z ≥ 0

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