ИДЗ 13.1 – Вариант 2. 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.

1.2. D: x2 = 2y, 5x - 2y - 6 = 0

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

 D: y = x2, y = 2x

3. Calculate the double integral using polar coordinates.

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

4.2. D: y = 6x2, x + y = 2, x ≥ 0

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

5.2. (X2 + y2) 3 = a2x2y2

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

6.2. z = 2 - (x2 + y2), x + 2y = 1, x ≥ 0, y ≥ 0, z ≥ 0

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