DHS 13.1 - Option 12. 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.

1.12. D: x = √2 - y2, x = y2, y ≥ 0

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

 D: y = 2x3, y = 0, x = 1

3. Calculate the double integral using polar coordinates.

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

4.12. D: y = x2, y = -x

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

5.12. (X2 + y2) 2 = 2a2xy

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

6.12. z = 10 + x2 + 2y2, y = x, x = 1, y ≥ 0, z ≥ 0