Area of Region (1 Viewer)

[xwrathbringerx]

ketch 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?

 

[Trebla]

ketch 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?

If you did straight integration, you wouldn't have accounted for the bottom half of the loop (draw a diagram to see this)