Area of Region (1 Viewer)

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xwrathbringerx

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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

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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)
 

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