ИДЗ 13.2 – Вариант 21. 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

1.21. V: x ≥ 0, y ≥ 0, z ≥ 0, x + y = 2, z = 4 - x2 - y2

2. Calculate the data triple integrals.

  V: 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, -1 ≤ z ≤ 3

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

, Υ: 1 ≤ x2 + y2 + z2 ≤ 9, y ≥ 0, y ≤ 1 / √3x, z ≥ 0

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

4.21. z ≥ 0, x2 + y2 = 9, z = y2

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