question_answer

    The area bounded by the curve\[y=2x-x\] and the straight line\[y=-x\]is given by:

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

B)  \[\frac{43}{6}\]

C)  \[\frac{35}{6}\]                               

D)  none of these

Correct Answer: A

Solution :

                Required Area \[=\int_{0}^{3}{({{y}_{1}}-{{y}_{2}})}dx\] \[=\int_{0}^{3}{(2x-{{x}^{2}})-(-x)dx}\]                 \[=\int_{0}^{3}{(3x-{{x}^{2}})dx}\]                 \[=\left[ \frac{3{{x}^{2}}}{2}-\frac{{{x}^{3}}}{3} \right]_{0}^{3}\]                 \[=\frac{27}{2}-9\]                 \[=\frac{9}{2}\]