Question

Area of the region bounded by the curve $ y=x,\text{ }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}{x\,dx}=\left| \int_{-1}^{0}{x\,dx} \right|+\left| \int_{0}^{2}{x\,dx} \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.