Find the area of the region in the first quadrant enclosed by x-axis, line and the circle x2 + y2 = 4.


The equations are and the circle


From the figure we can see that the x-axis is the area OAB and it si shown by shaded region.


Now, the point of intersection of the line and the circle in the first quadrant is .


Area OAB = Area ΔOCA + Area ACB


Area of ΔOCA =


Also,


Area of ABC =







Therefore, required area is = .


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