by interpreting it in terms of areas.
A definite integral can be interpreted as a net area, that is, a difference of areas;
where A1 is the region above x- axis and below the graph of f, and A2 is the region below x- axis and above the graph of f.
2) The property of integral
Area of semi-circle = A=12(πr2)
By using property of integral,
Now, draw the graph for each part separately.
First, drawgraph of fx= x in the given domain.
The graph of y=x is the line with slope 1 as shown below.
From the above graph, the areas A1 and A2 are symmetric about the origin since the shaded area above the x axis is the same as the shaded area below the x axis. So, the net area will be zero.
Now, draw graph of f(x)= 25-x2 in the given domain.
The graph of y=25-x2 in the given domain is as shown below which is a semi-circle with radius 5.
From the above graph,
Since diameter is 10 and the radius is half of diameter, the radius is 5.