Question

The area bounded by the curve $y=x,x$-axis and ordinates $x=-1$ to $x=2$ is :

• A. $0$
• B. $\frac{1}{2}$
• C. $\frac{3}{2}$
• D. $\frac{5}{2}$

Answer 1

The correct option is D $\frac{5}{2}$

Bounded area $=|{\int }_{-1}^{0}xdx|+|{\int }_0^{2}xdx|$

$={\left|\frac{x^2}{2}\right|}_{-1}^0+{\left|\frac{x^2}{2}\right|}_0^2$
$=|-\frac{1}{2}|+|2|=2+\frac{1}{2}=\frac{5}{2}$