ИДЗ 13.2 – Вариант 20. 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

1.20. V: x ≥ 0, y ≥ 0, z ≥ 0, 3x + 2y = 6, z = x2 + y2

2. Calculate the data triple integrals.

  V: -1 ≤ x ≤ 2, 0 ≤ y ≤ 1, 1 ≤ z ≤ 2

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

, Υ: x2 + y2 = 2x, x2 + y2 = 4x, z ≥ 0, z = 4, y ≥ 0, y ≤ x

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

4.20. y ≥ 0, z ≥ 0, y = 4, z = x, x = √25 - y2

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