Question

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

• A. $\frac{8}{3}$
• B. $\frac{49}{3}$
• C. $\frac{16}{3}$
• D. $\frac{14}{3}$

Answer 1

Answer: (B)

We have,
$y=\sqrt{x}, \,x=\sqrt{y},\, x=1,\, x=4$
The graph of curves are

Area of shaded region
$ =\int\limits_{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)$
$=\frac{64-16-1+2}{3}=\frac{49}{3}$