Sketch the curve defined by y^2 = x^2(1-x) and find the area of the loop.

1) Is the area of the loop the area between the curve and the X-axis between x=0 and x=1?

2) I keep on getting an area of 4/15 units^2 but the txtbk says it is 8/15 units^2. Am I wrong? If I am, could someone please show me the correct way to find the area?