Question

Area of the region (in sq units) bounded by the curves $y=\sqrt{x},x=\sqrt{y}$ and the lines $x=1x=4$, 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
$=\underset{1}{\overset{4}{\int }}\left(x^2-\sqrt{x}\right)dx={\left[\frac{x^3}{3}-\frac{2}{3}(x{)}^{3/2}\right]}_1^4$
$=\left(\frac{64}{3}-\frac{16}{3}\right)-\left(\frac{1}{3}-\frac{2}{3}\right)$
$=\frac{64-16-1+2}{3}=\frac{49}{3}$