Question

Find the area of the region bounded by the curve $y^2=x$ and the lines $x=1,x=4$ and the x-axis.

• A. $\frac{8}{3}$
• B. $\frac{14}{3}$
• C. $\frac{7}{3}$
• D. $\frac{1}{3}$

Answer 1

The correct option is B $\frac{14}{3}$

Required area = Area of ABCD = ${\int }_1^{4}ydx$

$={\int }_1^4\sqrt{x}dx$

$=\frac{2}{3}\left[\right(4{)}^{3/2}-\left(1{)}^{3/2}\right]$

$=\frac{2}{3}(8-1)=\frac{14}{3}$ units