The area bounded by the parabola $x^{2} = 8 y$ and line $x - 2 y + 8 = 0$ is-

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Solution

The correct option is A 36
Solving parabola $x^{2} = 8 y$
and line $x - 2 y + 8 = 0$ ,
we get
$x^{2} = 4 (x + 8)$
$\Rightarrow x = 8, - 4$
$∴$ Area of shaded region
$= \frac{1}{2} [8 + 2] \times 12 - \int_{- 4}^{8} \frac{x^{2}}{8} d x$
$= 60 - \frac{1}{8} . \frac{x^{3}}{3} |_{- 4}^{8} = 60 - 24 = 36$

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