Question

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

• A. $\frac{28}{3}$
• B. $4$
• C. $\frac{7}{3}$
• D. $\frac{4}{3}$

Answer 1

The correct option is A $\frac{28}{3}$


Area, $A={\int }_1^{4}ydx$
$={\int }_1^4\sqrt{4x}dx$
$=2{\int }_1^4\sqrt{x}dx$
$=2{\left(\frac{2}{3}{x}^{\frac{3}{2}}\right)}_1^4$
$=\frac{4}{3}(4^{\frac{3}{2}}-1^{\frac{3}{2}})$
$=\frac{28}{3}$