Find the area of the region bounded?

Question

Find the area of the region bounded by the parabola y^2=x and the line x+y=2. 

 

Answer: 9/2

 

Please show all your work. 

Answer 1

x = 2 - y = f(y)
x = y^2 = g(y) [parabola opening to the right]

Intersections:

2 - y = y^2
y^2 + y - 2 = 0
(y+2)(y-1) = 0
y = -2,1

A = integral{-2,1}[(f(y)-g(y)) dy]

You should be able to take it from here, Sun.