Question

Area of the region bounded by curve $y=x^2-x$ and X-axis is $=$ ____________.

• A. $\frac{6}{5}$
• B. $\frac{1}{6}$
• C. $\frac{5}{6}$
• D. $\frac{1}{2}$

Answer 1

Answer: (B)

$\frac{1}{6}$

On X-axis we have $y=0$
$\therefore x^2-x=0$
$x(x-1)=0$
$\therefore x=0$ OR $x=1$
Hence we have $x=0$ then $y=0$ and $x=1$ then $y=0$
$\therefore$ Point of intersection of curves with X-axis are $(0,0)$ and $(1,0)$
Area A$=\left|\stackrel{1}{\underset{0}{\int }}ydx\right|$
$=\stackrel{1}{\underset{0}{\int }}(x^2-x)dx$
$=\left|{(\frac{x^3}{3}-\frac{x^2}{2})}_0^1\right|$
$=|\frac{1}{3}-\frac{1}{2}|$
$=\left|\frac{2-3}{6}\right|$
$=\left|\frac{-1}{6}\right|$
$=\frac{1}{6}$.