Question

How do you find the area enclosed by the curve `y^2 = x(1 - x)`?

Answer 1

`pi/4` areal units.

Explanation:

The equation can be reorganized as

(x-1/2)^2+y^2=(1/2)^2 that represents a circle of radius 1/2.

So, the area is #pi(1/2)^2=pi/4 areal units. See the graph.

graph{y^2-x(1-x)=0 [-2.5, 2.5, -1.25, 1.25]}