Question

The area bounded by y-1 =|x|, y=0 and $\left|x\right|$ =$\frac{1}{2}$ will be:

• A. $\frac{3}{4}$
• B. $\frac{3}{2}$
• C. $\frac{5}{4}$
• D. None of these

Answer 1

Answer: (C)

The given lines are,
$y-1=x,x\ge 0;y-1=-x,x<0$
$y=0;x=-\frac{1}{2},x<0;x=\frac{1}{2},x\ge 0$
so that the area bounded is as shown in the figure.
Required area $=2\underset{0}{\overset{1/2}{\int }}(1+x)dx$
$=2{\left(x+\frac{x^2}{2}\right)}_0^{1/2}$
$=2\left(\frac{1}{2}+\frac{1}{8}\right)=\frac{5}{4}$