Question

The area of the region bounded by the curve $y=2x-x^2$ and the straight line $y=-x$ is

• A. $\frac{9}{2}$ sq. units
• B. $9$ sq. units
• C. $\frac{7}{2}$ sq. units
• D. $7$ sq. units

Answer 1

The correct option is A $\frac{9}{2}$ sq. units

Required area:
$=\underset{0}{\overset{3}{\int }}(2x-x^2+x)dx={(\frac{3x^2}{2}-\frac{x^3}{3})}_0^3=\frac{27}{2}-\frac{27}{3}=\frac{27}{6}$
$=\frac{9}{2}$ sq. units