ИДЗ 13.2 – Вариант 9. 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

1.9. V: x = 5, y = x / 5, y ≥ 0; z ≥ 0, z = x2 + 5y2

2. Calculate the data triple integrals.

  V: -1 ≤ x ≤ 0, 2 ≤ y ≤ 3, 1 ≤ z ≤ 2

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

, Υ: y ≥ 0, y ≤ √3x, z = 3 (x2 + y2), z = 3

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

4.9. z ≥ 0, z = 4 - x, x = 2√y, y = 2√x

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