DHS 13.1 - Option 9. 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.

1.9. D: y2 = 2x, x2 = 2y, x ≤ 1

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

 D: y = 5x, y = x, x = 3

3. Calculate the double integral using polar coordinates.

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

4.9. D: x = √4 - y2, y = √3x, x ≥ 0

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

5.9. (X2 + y2) 2 = a2 (2x2 + 3y2)

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

6.9. z = 2x2 + y2, x + y = 4, x ≥ 0, y ≥ 0, z ≥ 0