ИДЗ 13.2 – Вариант 2. 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

1.2. V: x = 1, y = 3x, y ≥ 0; z ≥ 0, z = 2 (x2 + y2)

2. Calculate the data triple integrals.

  V: -1 ≤ x ≤ 2, 0 ≤ y ≤ 3, 2 ≤ z ≤ 3

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

, Υ: z ≥ 0, z = 2, y ≥ ± x, z2 = 4 (x2 + y2)

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

4.2. z = 4 - y2, x2 + y2 = 4, z ≥ 0

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