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Area of the region (in sq units) bounded by the curves $y=\sqrt{x}, x=\sqrt{y}$ and the lines $x=1$, $x=4$, is
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1694 Upvotes
Verified Answer
The correct answer is:
$\frac{49}{3}$
We have,
$$
y=\sqrt{x}, x=\sqrt{y}, x=1, x=4
$$
The graph of curves are
Area of shaded region
$$
\begin{aligned}
& =\int_1^4\left(x^2-\sqrt{x}\right) d x=\left[\frac{x^3}{3}-\frac{2}{3}(x)^{3 / 2}\right]_1^4 \\
& =\left(\frac{64}{3}-\frac{16}{3}\right)-\left(\frac{1}{3}-\frac{2}{3}\right) \\
& =\frac{64-16-1+2}{3}=\frac{49}{3}
\end{aligned}
$$
$$
y=\sqrt{x}, x=\sqrt{y}, x=1, x=4
$$
The graph of curves are
Area of shaded region
$$
\begin{aligned}
& =\int_1^4\left(x^2-\sqrt{x}\right) d x=\left[\frac{x^3}{3}-\frac{2}{3}(x)^{3 / 2}\right]_1^4 \\
& =\left(\frac{64}{3}-\frac{16}{3}\right)-\left(\frac{1}{3}-\frac{2}{3}\right) \\
& =\frac{64-16-1+2}{3}=\frac{49}{3}
\end{aligned}
$$
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