DHS 13.1 - Option 30. 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.

1.30. D: x ≥ 0, y ≥ 0, y = 1, x = √4 - y2

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

 D: y = lnx, y = 0, x = 2

3. Calculate the double integral using polar coordinates.

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

4.30. D: xy = one, x2 = y, y = 2, x = 0.

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

5.30. ρ = asin3φ

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

6.30. y2 = x, x = 3, z = x, z ≥ 0