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]}