Question

The area bounded by the parabola $2y=x^2$ and the line $x=y-4$ is equal to

• A. $6$
• B. $18$
• C. $\infty$
• D. None of the above

Answer 1

The correct option is B $18$

$2y=x^2$
$x=y-4$
$\Rightarrow x^2=2x+8$
$\Rightarrow x^2-2x-8=0$
$x=4,-2$



Shaded area is required area and is given by
$={\int }_{x=-2}^4{\int }_{y=\frac{x2}{2}}^{x+4}\left(1\right)dydx$
$={\int }_{-2}^4(x+4-\frac{x^2}{2})dx$
$={[\frac{x^2}{2}+4x-\frac{x^3}{6}]}_{-2}^4$
$=18$