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The area (in. Sq. Units) bounded by the curve $y = 2 x - x^{2}$ and the line $y = - x$ is

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$\frac{9}{2}$

$\frac{11}{2}$

$\frac{16}{3}$

$\frac{22}{5}$

answer is A.

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Detailed Solution

$y = 2 x - x^{2} \to (1), y = - x \to (2)$
Solve (1) & (2)
$\begin{aligned} \Rightarrow 2 x - x^{2} = - x \Rightarrow x^{2} - 3 x = 0 \\ x = 0 (or) x = 3 \\ Area = \int_{0}^{3} [(2 x - x^{2}) - (- x)] d x = \frac{9}{2} \end{aligned}$

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