Area lying in first quadrant and bounded by the circle x² + y² = 4 and the lines x = 0 and x = 2, is

The part of the circle x² + y² = 4 in between x = 0 and x = 2 is the semicircle to the right of the y – axis.

And the part of this semicircle in the first quadrant is a quadrant of the circle.

So, area A of the portion is basically the area of a quadrant of the circle.

∴ A = πr²/4

= π × 2²/4

= π (Ans)