ИДЗ 13.1 – Вариант 6. 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.

1.6. D: y = √2 - x2, y = x2

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

 D: y = x, y = x2

3. Calculate the double integral using polar coordinates.

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

4.6. D: y = x2 + 1, x + y = 3

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

5.6. ρ = asin22φ

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

6.6. z = x, y = 4, x = √25 - y2, x ≥ 0, y ≥ 0, z ≥ 0

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