Question

The area bounded by the parabola $y^2=x$ and the straight line $2y=x$ is

• A. $\frac{4}{3}$
• B. $1$
• C. $\frac{2}{3}$
• D. $\frac{1}{3}$

Answer 1

The correct option is A $\frac{4}{3}$

$y^2=x$, 2y=x

point of intersection

$(\frac{x}{2}{)}^2=x$

x=0,4

y=0,2

$Area={\int }_0^4\sqrt{x}dx-{\int }_0^4\left(\frac{x}{2}\right)dx$

$\frac{2}{3}{\left[x^{\frac{3}{2}}\right]}_0^4-{\frac{x^2}{4}}_0^4$

$=\frac{2\ast 8}{3}-4$

$=\frac{4}{3}squnit$