ИДЗ 13.2 – Вариант 3. 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

1.3. V: x = 1, y = 4x, z ≥ 0, z = √3y

2. Calculate the data triple integrals.

  V: -1 ≤ x ≤ 1, 0 ≤ y ≤ 2, -1 ≤ z ≤ 1

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

, Υ: 1 ≤ x2 + y2 ≤ 36, y ≥ x, x ≥ 0, z ≥ 0

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

4.3. x2 + y2 = 1, z = 2 - x - y, z ≥ 0

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