plane areas in rectangular coordinates (please help)

Question

Find the area bounded by the curve:

y = x(x-1)^2, the line y = 2, and the y - axis

Answer 1

Hi Kim,

 

Take a look at this graph to get the idea: https://www.desmos.com/calculator/lkvil0oqhm

 

The vertical red strip represents a "typical" rectangle with a height that can be represented by 2 - f(x). 

 

So, ∫₀² (2 - f(x))dx where f(x) = x(x-1)² should to the trick. Notice that when x=2, y=2 (the point of intersection of y=2 with f(x).