Question

Area of the region bounded by the curve $y=x,x-$ axis and abscissas $x=-1$ and $x=2$ is

• A. 0 sq unit
• B. 3/2 sq unit
• C. 5/2 sq units
• D. - 5/2 sq unit

Answer 1

Answer: (C)

Area of the region bounded by the curve
$y=x,$ $x-$ axis and abscissae
$x=-1$ and $x=2$ is given by
$A={\int }_{-1}^{2}xdx=\left|{\int }_{-1}^{0}xdx\right|+\left|{\int }_0^{2}xdx\right|$
$=\left|{\left[\frac{x^2}{2}\right]}_{-1}^0\right|+\left|{\left[\frac{x^2}{2}\right]}_0^2\right|$
$=\left|0-\frac{1}{2}\right|+\left|\frac{4}{2}-0\right|$
$=\frac{1}{2}+2$
$=\frac{5}{2}$ sq units.