Question

Let f(x) = max {}, where .
Determine the area of the region bounded by the curves
y=f (x), X-axis, x = 0 and x = 1.

Answer 1

We can draw the graph of , and
y = 2 x (1 - x) in following figure
Now, to get the point of intersection of and y = 2x (1 - x), we get,

x(3x-2)=0 x = 0,
Similarly, we can find the coordinate of the points of
intersection of
and y = 2x (1 - x) are and x=1
From the figure, it is clear that,

The required area


+
=++
sq unit