ИДЗ 13.2 – Вариант 8. 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

1.8. V: x ≥ 0, y = 3x, y = 3; z ≥ 0, x = 3√z

2. Calculate the data triple integrals.

  V: 0 ≤ x ≤ 3, -2 ≤ y ≤ 0, 1 ≤ z ≤ 2

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

, Υ: x ≥ 0, z ≥ 0, y ≥ √3x, 4 ≤ x2 + y2 + z2 ≤ 36

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

4.8. x ≥ 0, z ≥ 0, z = y, x = 4, y = √25 - x2

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