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  4. The area bounded by the parabola y2 = x straight line y = 4 and y -axis is square units is

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Q. The area bounded by the parabola $ y^2 = x $ straight line $ y = 4 $ and $ y $ -axis is square units is

MHT CETMHT CET 2011

Solution:

Line $y=4$ meets the parabola $y^{2}=x$ at $A$
$\therefore 16=x$ and $A$ is (16,4)
image
$\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}
$