Question

The area of the region enclosed by the curves y = x log x and $y=2x–2x^2$ is

• A. $\frac{5}{12}$
• B. $\frac{7}{12}$
• C. $\frac{1}{12}$
• D. Not defined

Answer 1

The correct option is B $\frac{7}{12}$

$A={\int }_0^1(2x-2x^2-xlogx)dx$
$={[x^2-\frac{2x^3}{3}-\frac{x^2}{x}logx+\frac{x^2}{4}]}_0^1$
$=1-\frac{2}{3}+\frac{1}{4}=\frac{7}{12}$