Question #4597

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

Expert's answer

Let's transform our system:

x = y^{2}/2, x = y +4;

and change variables:

y = x^{2}/2, y = x +4.

Let’s find the points of interception: x^{2}/2=x+4x^{2}/2-x-4=0 x=4 or x=-2

S= Integral(x+4-x^{2}/2)dx |_{x=-2} ^{x=4}=(x^{2}/2+4x-x^{3}/6) |_{x=-2} ^{x=4}=18

x = y

and change variables:

y = x

Let’s find the points of interception: x

S= Integral(x+4-x

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