I obtained the same integral and the same result 32/3. All is ok
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:
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