ИДЗ 13.2 – Вариант 6. 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

1.6. V: x = 0, y = x, y = 5; z ≥ 0, z = 2x2 + y2

2. Calculate the data triple integrals.

  V: 0 ≤ x ≤ 1, -1 ≤ y ≤ 0, 1 ≤ z ≤ 2

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.

4.6. x2 + y2 = 4, z = 4 - x - y, z ≥ 0

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