ИДЗ 13.1 – Вариант 13. 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.

1.13. D: y ≥ 0, x + 2y - 12 = 0, y = lgx.

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

 D: x = y2, x = 1

3. Calculate the double integral using polar coordinates.

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

4.13. D: x = y2, x = 3 / 4y2 + 1

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

5.13. (X2 + y2) 3 = 4x2y2

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

6.13. z = x2, x + y = 6, y = 2x, x ≥ 0, y ≥ 0, z ≥ 0

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