The area bounded by the curve y = 4x – x2 and the x-axis is
y = 4x – x2
This is a parabola with negative co-efficient of x2, i.e., it’s a downward parabola.
So, area A enclosed is the area of the peak of the parabola above the x – axis.
We need to find the bounds of this peak.
Now, at the point where the peak starts/ends, y = 0,
i.e., 4x – x2 = 0
⇒ x(4 – x) = 0
⇒ x = 0 or x = 4
∴ A =
= [32 – 64/3]
= 32/3 sq. units (Ans)