Determine the area under the curve y=, included between the lines x=0 and x=4.
Given the boundaries of the area to be found are,
• The curve
• x = 0 (y-axis)
• x = 4 (a line parallel toy-axis)
Here the curve, , can be re-written as
----- (1)
This equation (1) represents a circle equation with (0,0) as center and, a units as radius.
As x and y have even powers, the given curve will be about the x-axis and y-axis.
As per the given boundaries,
• The curve, is a curve with vertex at (0,0).
• x=4 is parallel toy-axis at 4 units away from the y-axis. (but this might not really effect the boundaries as the value of ‘a’ in the equation is unknown.)
• x=0 is the y-axis.
Area of the required region = Area of OBC.
[Using the formula, ]
[sin-1(1) = 90° and sin-1(0) = 0° ]
The Area of the required region