DHS 13.1 - Option 1. 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.

1.1. D: y = √4 - x2, y = √3x, x ≥ 0

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

D: y = x2, x = y2

3. Calculate the double integral using polar coordinates.

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

4.1. D: y2 = 4x, x + y = 3, y ≥ 0

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

5.1. (X2 + y2) 2 = a2 (4x2 + y2)

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

6.1. z = x2 + y2, x + y = 1, x ≥ 0, y ≥ 0, z ≥ 0