Question

Find the area bounded by the curves x = y2 - 4y and x = 2y - y2. Your work must include an integral in one variable.

Answer 1

The curves x = y^2 - 4y and x = 2y - y^2 are two parabolas with vertices (-4,2) and (1,1), respectively.

The solutions (0,0) and (-3,3) of system $\left \{ {{x = y^2 - 4y } \atop {x = 2y - y^2 }} \right.$ give the common points of these parabolas.
The area is calculated in the image.