Question

The area bounded by the curve $y=\frac{x^2}{2}$ bounded by $x=0,x=2$ and $y=0$ is:

• A. $\frac{4}{5}$ sq. units
• B. $\frac{3}{2}$ sq. units
• C. $\frac{3}{4}$ sq. units
• D. $\frac{4}{3}$ sq. units

Answer 1

The correct option is D $\frac{4}{3}$ sq. units

$y=\frac{x^2}{2}$
Area of shaded region=$\stackrel{2}{\underset{0}{\int }}ydx$
=$\stackrel{2}{\underset{0}{\int }}\frac{x^2}{2}dx$

$=x^3/6{|}_0^2$

$=8/6=4/3squnits$.