ИДЗ 13.1 – Вариант 20. 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.

1.20. D: y ≤ 0, x2 = -y, x = √1 - y2

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

 D: y = x2 - 1, y = 3

3. Calculate the double integral using polar coordinates.

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

4.20. D: y = 4 - x2, y = x2 - 2x

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

5.20. (X2 + y2) 3 = a2x2y2

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

6.20. z = 2x2 + y2, x + y = 1, x ≥ 0, y ≥ 0, z ≥ 0

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