ИДЗ 13.2 – Вариант 4. 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

1.4. V: x = 3, y = x, y ≥ 0; z ≥ 0, z = 3x2 + y2

2. Calculate the data triple integrals.

  V: 0 ≤ x ≤ 3, -1 ≤ y ≤ 2, 0 ≤ z ≤ 2

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

, Υ: x2 + y2 + z2 = 32, y2 = x2 + z2, y ≥ 0

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

4.4. z = y2, x ≥ 0, z ≥ 0, x + y = 2

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