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
$=\underset{0}{\overset{2}{\int }}\left[(x+2)-\left(x^2-x+2\right)\right]dx$
$=\underset{0}{\overset{2}{\int }}\left(-x^2+2x\right)dx$
$={\left[-\frac{x^3}{3}+x^2\right]}_0^2=-\frac{8}{3}+4$
$=\frac{4}{3}$ sq unit