1. Find the area lying in the first quadrant and bounded by the circle \({x^2} + {y^2} = 4\) and the lines \(x = 0\) and \(x = 2\).

2. Find the area of the region bounded by the curve \({y^2} = 4x\), y-axis and the line \(y = 3\).

3. Find the area of the region bounded by the two parabolas \(y = {x^2}\) and \({y^2} = x\).

4. Find the area lying above x-axis and included between the circle \({x^2} + {y^2} = 8x\) and the parabola \({y^2} = 4x\).

5. In figure, AOBA is the part of the ellipse \(9{x^2} + {y^2} = 36\) in the first quadrant such that \(OA = 2\) and \(OB = 6\). Find the area between the arc AB and the chord AB.

6. Using integration find the area of region bounded by the triangle whose vertices are (1, 0), (2, 2) and (3, 1).