question_answer

The area of figure bounded by the curve  \[y=2x-{{x}^{2}}\] and the straight line \[y=-x\] is

A)  \[\frac{9}{2}\]                                  

B)  9

C)  \[\frac{7}{2}\]                                  

D)  7

Correct Answer: A

Solution :

Area\[=\int\limits_{0}^{3}{(2x-{{x}^{2}})-xdx=}\int\limits_{0}^{3}{(x-{{x}^{2}})dx=\frac{9}{2}}\]