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

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Answer 1 · 2016-12-11T12:06:56

$\frac{π}{4}$ $pi/4$ areal units.

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]}

How do you find the area enclosed by the curve y2=x(1−x)y^2 = x(1 - x)?