The area between


The area between $x=y^{2}$ and $x=4$ is divided into two equal parts by the line $x=a$, find the value of $a$.


The line, $x=a$, divides the area bounded by the parabola and $x=4$ into two equal parts.

$\therefore$ Area $\mathrm{OAD}=$ Area $\mathrm{ABCD}$

It can be observed that the given area is symmetrical about x-axis.

⇒ Area OED = Area EFCD

Area of EFCD $=\int_{a}^{4} \sqrt{x} d x$


$=\frac{2}{3}\left[8-a^{\frac{3}{2}}\right]$               ...(2)

From (1) and (2), we obtain


$\Rightarrow 2 \cdot(a)^{\frac{3}{2}}=8$


$\Rightarrow a=(4)^{\frac{2}{3}}$

Therefore, the value of $a$ is $(4)^{\frac{2}{3}}$.





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