Question

The area bounded by the curve $y=2x-x^2$ and the straight line $y+x=0$ is given by:

• A. $\frac{9}{2}$
• B. $\frac{43}{6}$
• C. $\frac{35}{6}$
• D. None of these

Answer 1

Answer: (A)

$\frac{9}{2}$

From figure required area $={\int }_0^2(2x-x^2)dx-{\int }_2^3\left(2x-x^2-(-x)\right)dx$
$={\int }_0^2(2x-x^2)dx-{\int }_2^3(3x-x^2)dx={[\frac{2x^2}{2}-\frac{x^3}{3}]}_0^2-{[\frac{3x^2}{2}-\frac{x^3}{3}]}_2^3=\frac{9}{2}$