ИДЗ 13.2 – Вариант 15. 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

1.15. V: x ≥ 0, y = 5x, y = 10; z ≥ 0, z = x2 + y2

2. Calculate the data triple integrals.

  V: -1 ≤ x ≤ 2, 0 ≤ y ≤ 1, 0 ≤ z ≤ 1

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

, Υ: x2 + y2 = 16y, y + z = 16, x ≥ 0, z ≥ 0

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

4.15. z ≥ 0, y = √9 - x2, z = 2y

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