Question

The area bounded by the curves, $y=|1-x|,y=|1+x|,y=2x^2,y=0$ is

• A. $\frac{5}{18}\text{sq. units}$
• B. $\frac{5}{12}\text{sq. units}$
• C. $\frac{5}{24}\text{sq. units}$
• D. $\frac{5}{6}\text{sq. units}$

Answer 1

The correct option is B $\frac{5}{12}\text{sq. units}$


$\text{Required area}=2\left[{\int }_0^{\frac{1}{2}}2x^{2}dx+{\int }_{\frac{1}{2}}^1(1-x)dx\right]$
$=2({\left[\frac{2x^3}{3}\right]}_0^{\frac{1}{2}}+{[x-\frac{x^2}{2}]}_{\frac{1}{2}}^1)=\frac{5}{12}$