Area between parabola x = y² and line 2y + x = 3

[Kuma]

Homework Statement

Alright so the problem:

Find the reigon in the xy plane that is bounded by the curves:

x = y^2
and
2y + x = 3


quickly solving for the y coordinates of intersection, i get
y = -3 and 1

so using horizontal components i got:

$$\int^{1}_{-3}$$ 3-2y - y^2

and then integrating and quickly solving i get 32/3 as a final answer
do the steps seem alright or have i made a mistake somewhere?

Many thanks :)

 

[mutton]

That's right.