Answer is 18 sq units.
2y = x^2 and x = y - 4 ....... eqA
Now,
x^2 = 2 ( x + 4 ) ......eq2
Solving eq2 we get x = 4 , - 2.
Place Values of x in eqA we get y = 8 , 2.
Thus, the points of intersection are (8, 4), (2, –2)
Area = Integration from -2 to 4 on ( x - ( x^2 / 2 ) + 4 ) dx
Solve Integration we get Answer as 18