ИДЗ 13.2 – Вариант 25. 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

1.25. V: x = 2, y ≥ 0, z ≥ 0, y = 3x, z = 4 (x2 + y2)

2. Calculate the data triple integrals.

  V: 0 ≤ x ≤ 2, -1 ≤ y ≤ 0, 0 ≤ z ≤ 4

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

, Υ: 4 ≤ x2 + y2 + z2 ≤ 16, y ≤ √3x, y ≥ 0, z ≥ 0

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

4.25. z ≥ 0, y + z = 2, x2 + y2 = 4

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