DHS 13.1 - Option 4. 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.

1.4. D: x ≥ 0, y ≥ 0, y ≤ 1, y = lnx

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

 D: y = 2 - x, y = x, x ≥ 0

3. Calculate the double integral using polar coordinates.

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

4.4. D: x = -2y2, x = 1 - 3y2, x ≤ 0, y ≥ 0

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

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

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

6.4. z = 2x2 + 3y2, y = x2, y = x, z ≥ 0