ИДЗ 13.1 – Вариант 23. 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.

1.23. D: y = 3 - x2, y = -x

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

 D: x + y = 1, x + y = 2, x ≤ 1, x ≥ 0

3. Calculate the double integral using polar coordinates.

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

4.23. D: x = cosy, x ≤ y + 1, x ≥ 0

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

5.23. (X2 + y2) 3 = 4a2xy (x2 - y2)

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

6.23. y = 1 - z2, y = x, y = -x, y ≥ 0, z ≥ 0

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