ИДЗ 13.2 – Вариант 12. 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

1.12. V: x = 4, y = x / 4, z ≥ 0, z = 4y2

2. Calculate the data triple integrals.

  V: 0 ≤ x ≤ 1, 0 ≤ y ≤ 2, -1 ≤ z ≤ 3

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

, Υ: z = x2 + y2, y ≥ 0, y ≤ x, z = 4

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

4.12. x ≥ 0, z ≥ 0, y = 2x, y = 3, z = √y

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