ИДЗ 13.2 – Вариант 30. 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

1.30. V: x ≥ 0, y ≥ 0, z ≥ 0, 5x + y = 5, z = x2 + y2

2. Calculate the data triple integrals.

  V: 0 ≤ x ≤ 3, 0 ≤ y ≤ 1, -2 ≤ z ≤ 1

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

, Υ: z = √18 - x2 - y2, z = √x2 + y2, x ≥ 0

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

4.30. x ≥ 0, z ≥ 0, x + y = 4, z = 4√y

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