How do you sketch the region enclosed by $y=x^2, y^2=x$ and find the area?

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Answer 1 · 2017-01-26T08:03:50

$1/3$ areal units.

The common points are (0, 0) and (1, 1).

$y^2 = x>=0 and x^2=y>=0$ .

So, the petal-like common area is between O and (1, 1)

Area = $int$ (y-difference) dx, with x from 0 to 1.

$= int (sqrtx-x^2) dx$ ,with x from 0 to 1.

$=[2/3x^(3/2)-x^3/3]$ , between x = 0 and 1.

#=1/3, areal units.

graph{(y-x^2)(y^2-x)=0 [-2.51, 2.51, -1.255, 1.255]}

How do you sketch the region enclosed by y=x^2, y^2=xy=x^2, y^2=x and find the area?