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**iiharthero** find the area of the loop defined by y^2=x^2(1-x)

im quite confused with this question because im not really sure what the "loop" really refers to, i graphed the curve and assumed that the loop referred to when x is between 1 and 0. I then proceeded to find y in terms of x which i THINK becomes y=x[sqrt(1-x)]. After this, i integrated the equation using u substitution but my answer was 4/15 and not, as the answer says, 8/15.

If anyone could direct me on where i went wrong, that would be a great help. thank you for your time and effort.