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The area bounded by the parabola $y^{2}=x$, straight line $y=4$ and $y$ -axis is square units is
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1865 Upvotes
Verified Answer
The correct answer is:
$64 / 3$ sq. unit
Line $y=4$ meets the parabola $y^{2}=x$ at $A$
$\therefore \quad 16=x$ and $A$ is $(16,4)$
$\therefore$ Required area
$$
\begin{array}{l}
=\int_{y=0}^{4} x d y \\
=\int_{y=0}^{4} y^{2} d y \\
=\left[y^{3} / 3\right]_{0}^{4} \\
=\frac{64}{3} \text { sq units }
\end{array}
$$
$\therefore \quad 16=x$ and $A$ is $(16,4)$
$\therefore$ Required area
$$
\begin{array}{l}
=\int_{y=0}^{4} x d y \\
=\int_{y=0}^{4} y^{2} d y \\
=\left[y^{3} / 3\right]_{0}^{4} \\
=\frac{64}{3} \text { sq units }
\end{array}
$$
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