ИДЗ 13.1 – Вариант 10. 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.

1.10. D: x ≥ 0, y ≥ x, y = √9 - x2

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

 D: y = x, y = 1 / 2x, x = 2

3. Calculate the double integral using polar coordinates.

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

4.10. D: y = x2 + 2, x ≥ 0, x = 2, y = x

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

5.10. (X2 + y2) 2 = a2 (5x2 + 3y2)

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

6.10. z = 4 - x2, x2 + y2 = 4, x ≥ 0, y ≥ 0, z ≥ 0

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