ИДЗ 13.2 – Вариант 22. Решения Рябушко А.П.

1. Arrange the limits of integration in the triple integral, if the area is limited to V said surfaces. Draw the region of integration

1.22. V: x ≥ 0, y ≥ 0, z ≥ 0, x + y = 3, z = 9 - x2 - y2

2. Calculate the data triple integrals.

  V: 0 ≤ x ≤ 1, -1 ≤ y ≤ 2, 0 ≤ z ≤ 3

3. Evaluate the triple integral using cylindrical or spherical coordinates.

, Υ: x2 - 2x + y2 = 0, y ≥ 0, z ≥ 0, x + z = 2

4. Use a triple integral to calculate the volume of the body bounded by said surfaces. Make a drawing.

4.22. x ≥ 0, z ≥ 0, y ≥ x, z = 1 - x2 - y2

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