Question

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

Answer 1

x=y^2-4y
add 4 to both sides
x+4=y^2-4y+4
(y-2)^2=(x+4)
so vertex of this parabola is (-4,2)
x=2y-y^2
y^2-2y=-x
y^2-2y+1=-x+1
(y-1)^2=-(x-1)
vertex of this parabola is (1,1)