Question

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

• A. 8/3
• B. 1/3
• C. 2/3
• D. 4/3

Answer 1

Answer: (D)

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