Calculate the area of the bounded region between the curves y^2=x and 3y = -3y + 9 ?

3 answers

3y = -3y + 9 ???
Fix that.

Then, find where the two graphs intersect. Since the parabola opens to the right, it's easier to integrate along dy. The area is just a bunch of thin strips of height dy and length the distance between the two curves. Express that and integrate from bottom to top.
3y = -3x + 9
the curves intersect at y = (-1-√13)/2 and (-1+√13)/2

area is thus

∫[(-1-√13)/2,(-1+√13)/2] (-y+3)-(y^2) dy