Question

The area enclosed between the parabola $y = x^2-x+2$ and the line $y=x+2$ in sq units =

• A. $\frac {4}{3}$
• B. $\frac {2}{3}$
• C. $\frac {-1}{3}$
• D. $\frac {8}{3}$

Answer 1

Answer: (A)

Given equation of parabola is

$y=x^{2}-x+2$
or $\left(x-\frac{1}{2}\right)^{2} =y-\frac{7}{4}$
and equation of line is
$y=x+2$
$\therefore $ Required area
$=\int\limits_{0}^{2}\left[(x+2)-\left(x^{2}-x+2\right)\right] d x $
$=\int\limits_{0}^{2}\left(-x^{2}+2 x\right) d x $
$=\left[-\frac{x^{3}}{3}+x^{2}\right]_{0}^{2}=-\frac{8}{3}+4$
$=\frac{4}{3} $ sq unit