DHS 13.1 - Option 25. 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.

1.25. D: x = 0, y = 0, y = 1, (x - 3) 2 + y2 = 1

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

 D: x + y = 1, y = x2 - 1, x ≥ 0

3. Calculate the double integral using polar coordinates.

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

4.25. D: x = y2, x = √2 - y2

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

5.25. ρ = acos5φ

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

6.25. x2 + y2 = 1, z = 2 - x2 - y2, z ≥ 0