Answer:
y^2 = 2x + 6
2x = y^2 - 6
x = 1/2(y^2 - 6)
The points of intersection of the curves are calculated:
y + 1 = 1/2( y^2 - 6)
2y + 2 = y^2 - 6
y^2 - 2y - 8 = 0
( y - 4)(y + 2) = 0
y = 4, -2
when y = 4, x = 5 and when y = -2 x = -1.
Integrating between y = 4 and y = -2
4
INT [ ( y + 1 + 1/2 (6 - y^2) ]dy
-2
= 4
{ y^2 / 2 + y + 3y - y^3/6 }
-2
= 13 1/3 - (-4 2/3)
13 1/3 + 4 2/3
= 18 answer.
