Answer to Question #4597 in Integral Calculus for Rodel john

Question

find the area bounded by the y² = 2x, y = x - 4.

Answer 1

Let's transform our system:
x = y²/2, x = y +4;
and change variables:
y = x²/2, y = x +4.
Let’s find the points of interception: x²/2=x+4x²/2-x-4=0 x=4 or x=-2
S= Integral(x+4-x²/2)dx |_x=-2 ^x=4=(x²/2+4x-x³/6) |_x=-2 ^x=4=18