DHS 13.1 - Option 16. Decisions Ryabushko AP

1. Provide a double integral as an iterated integral with the outer integration over x and external integration with respect to y, if D is given the above lines.

1.16. D: y ≥ 0, x = √y, y = √8 - x2.

2. Calculate the double integral over the region D, limited to lines.

 D: y = 1 - x2, y ≥ 0

3. Calculate the double integral using polar coordinates.

4. Calculate the area of a plane region D, bounded set tench.

4.16. D: 2y = √x, x + y = 5, x ≥ 0

5. Use double integrals in polar coordinates to calculate the flat area of the figure bounded by the lines indicated.

5.16. ρ = acos2φ

6. Calculate the volume of the body bounded by a given surface.

6.16. y2 = 1 - x, x + y + z = 1, x = 0, z = 0