Question

Area bounded by the parabola $y^2=x-3$ and $x=5$, is ....$sq$ units

• A. $\frac{8\sqrt{2}}{3}$
• B. $4\sqrt{2}$
• C. $3\sqrt{2}$
• D. $5\sqrt{2}$

Answer 1

Answer: (A)

$\frac{8\sqrt{2}}{3}$

$y^2=x-3$ , $x=5$

$A=(3,0)$ , $B=(5,\sqrt{2})$ , $C=(5,-\sqrt{2})$

$={\int }_3^5\sqrt{x-3}dx$

$=\frac{2}{3}\left[\right(x-3{)}^{\frac{3}{2}}{]}_3^5$

$=\frac{2^{\frac{5}{2}}}{3}squnits$