ИДЗ 13.1 – Вариант 8. 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.

1.8. D: x ≥ 0, y ≥ 1, y ≤ 3, y = x

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

 D: y = x2 - 1, y = -x2 + 1

3. Calculate the double integral using polar coordinates.

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

4.8. D: y = cosx, y ≤ x + 1, y ≥ 0

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

5.8. ρ = a (1 - cosφ)

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

6.8. y = 1 - x2, x + y + z = 3, y ≥ 0, z ≥ 0