DHS 13.2 - Option 11. Decisions Ryabushko AP

1. Arrange the limits of integration in the triple integral, if the area is limited to V said surfaces. Draw the region of integration

1.11. V: x = 3, y = 1 / 3x, y ≥ 0; z ≥ 0, z = 1/2 (x2 + y2)

2. Calculate the data triple integrals.

  V: -2 ≤ x ≤ 0, 0 ≤ y ≤ 1, 0 ≤ z ≤ 2

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

, Υ: z = 2 (x2 + y2), y ≥ 0, y ≤ 1 / √3x, z = 18

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

4.11. y ≥ 0, z ≥ 0, x = 4, y = 2x, z = x2