Question

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

• A.
• B.
• C.
• D. not defined

Answer 1

The correct option is B

A = ${\int }_0^1$(2x - 2$x^2$ - xlogx)dx

= ${[x^2-\frac{2x^3}{9}-\frac{x^2}{x}logx+\frac{x^2}{4}]}_0^1$

= 1 - $\frac{2}{3}$ + $\frac{1}{4}$ = $\frac{7}{12}$($\therefore {lim}_{x\to 0}{x}^2.logx=0$)