ИДЗ 13.2 – Вариант 29. 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

1.29. V: x ≥ 0, y ≥ 0, z ≥ 0, x + y = 4, z = 16 - x2 - y2

2. Calculate the data triple integrals.

  V: 1 ≤ x ≤ 2, -2 ≤ y ≤ 3, 0 ≤ z ≤ 1

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

, Υ: 1 ≤ x2 + y2 + z2 ≤ 9, y ≤ x, y ≥ 0, z ≥ 0

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

4.29. x ≥ 0, y ≥ 0, z ≥ 0, y = 3 - x, z = 9 - x2

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