Find by integration the area bounded by the curve y2=4ax and the lines y=2a and x=0.
Given the boundaries of the area to be found are,
• The curve y2 = 4ax
• y = 2a (a line parallel to x-axis)
• x = 0 (y-axis)
As per the given boundaries,
• The curve y2 =4ax, has only the positive numbers as y has even power, so it is about the x-axis equally distributed on both sides.
• y= 2a is parallel to x-axis with 2a units from the x-axis.
The boundaries of the region to be found are,
•Point A, where the curve y2 = 4ax and y=2a meet i.e. A(2a,2a)
•Point B, where the curve y2 = 4ax and y-axis meet i.e. B(0,2a)
•Point O, is the origin
Consider the curve y2 = 4ax,
Area of the required region = Area of OBA.
[Using the formula ]
The Area of the required region