DHS 13.2 - Option 20. 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
1.20. V: x ≥ 0, y ≥ 0, z ≥ 0, 3x + 2y = 6, z = x2 + y2
2. Calculate the data triple integrals.
V: -1 ≤ x ≤ 2, 0 ≤ y ≤ 1, 1 ≤ z ≤ 2
3. Evaluate the triple integral using cylindrical or spherical coordinates.
, Υ: x2 + y2 = 2x, x2 + y2 = 4x, z ≥ 0, z = 4, y ≥ 0, y ≤ x
4. Use a triple integral to calculate the volume of the body bounded by said surfaces. Make a drawing.
4.20. y ≥ 0, z ≥ 0, y = 4, z = x, x = √25 - y2
1.20. V: x ≥ 0, y ≥ 0, z ≥ 0, 3x + 2y = 6, z = x2 + y2
2. Calculate the data triple integrals.
V: -1 ≤ x ≤ 2, 0 ≤ y ≤ 1, 1 ≤ z ≤ 2
3. Evaluate the triple integral using cylindrical or spherical coordinates.
, Υ: x2 + y2 = 2x, x2 + y2 = 4x, z ≥ 0, z = 4, y ≥ 0, y ≤ x
4. Use a triple integral to calculate the volume of the body bounded by said surfaces. Make a drawing.
4.20. y ≥ 0, z ≥ 0, y = 4, z = x, x = √25 - y2
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