Question

The area bounded by the line $y - x$ , x-axis and lines $x = -1$ to $x = 2$, is

• A. $0$ s unit
• B. $1/2$ s unit
• C. $3/2$ s unit
• D. $5/2$ s unit

Answer 1

Answer: (D)

$5/2$ s unit

Answer 2

We have $y=x$ Required area = area of shaded region $A=\left|\int\limits_{-1}^{0}x dx\right|+\left|\int\limits_{0}^{2}xdx\right|=\left|\frac{x^{2}}{2}\right|_{-1}^{0}+\left|\frac{x^{2}}{2}\right|_{0}^{2}$ $=\left|-\frac{1}{2}\right|+\left|2\right|=2+\frac{1}{2}=\frac{5}{2}$ s units