DHS 13.2 - Option 19. Decisions Ryabushko AP
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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
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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