ИДЗ 13.2 – Вариант 7. 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

1.7. V: x ≥ 0, y = 2x, y = 1; z ≥ 0, x + y + z = 3

2. Calculate the data triple integrals.

  V: 1 ≤ x ≤ 5, 0 ≤ y ≤ 2, -1 ≤ z ≤ 0

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

, Υ: z = √8 - x2 - y2, z = √x2 + y2, y ≥ 0

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

4.7. z ≥ 0, z = x2, x - 2y + 2 = 0, x + y = 7

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