ИДЗ 13.1 – Вариант 27. 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.

1.27. D: x + 2y - 6 = 0, y = x, y ≥ 0.

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

 D: y = x, xy = 1, y = 2

3. Calculate the double integral using polar coordinates.

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

4.27. D: y2 = 4 - x, y = x + 2, y = 2, y = -2

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

5.27. ρ = 2a (2 + cosφ)

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

6.27. z2 = 4 - x, x2 + y2 = 4x, z ≥ 0

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