ИДЗ 13.1 – Вариант 17. 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.

1.17. D: y = - x, y2 = x + 3.

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

 D: y3 = x, y = x

3. Calculate the double integral using polar coordinates.

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

4.17. D: y = 2x, y = 2x - x2, x = 2, x = 0

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

5.17. ρ2 = a2 (1 + sin2φ)

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

6.17. y = x2, x = y2, z = 3x + 2y + 6, z = 0

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