ИДЗ 13.2 – Вариант 19. 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

1.19. V: x ≥ 0, y ≥ 0, z ≥ 0, x + y = 1, z = 3x2 + 2y2

2. Calculate the data triple integrals.

  V: 0 ≤ x ≤ 4, 1 ≤ y ≤ 3, -1 ≤ z ≤ 5

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

, Υ: x2 + y2 + z2 = 36, y ≥ 0, z ≥ 0, y ≤ -x

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

4.19. y ≥ 0, z ≥ 0, x + y = 2, z = x2

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