ИДЗ 13.2 – Вариант 18. 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

1.18. V: y = x, y = -2x, y = 1; z ≥ 0, z = x2 + 4y2

2. Calculate the data triple integrals.

  V: 0 ≤ x ≤ 2, 1 ≤ y ≤ 2, -1 ≤ z ≤ 0

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

, Υ: x2 + y2 = 2y, x2 + y2 = 4y, x ≥ 0, z ≥ 0, z = 6

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

4.18. z ≥ 0, z = x, x = √4 - y2

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