question_answer

The area bounded by the curves \[y=3x\]and \[y={{x}^{2}}\]is (in square units)

A)  \[10\]            

B)  \[5\]

C)  \[4.5\]          

D)  \[9\]

Correct Answer: C

Solution :

Given curves are \[y=3x\] ?..(i) and \[y={{x}^{2}}\] ?.(ii) On solving Eqs. (i) and (ii), we get \[x=0,3\] Now, required area \[=\int_{0}^{3}{(3x-{{x}^{2}})\,dx}\] \[=\left[ \frac{3{{x}^{2}}}{2}-\frac{{{x}^{3}}}{3} \right]_{0}^{3}\] \[=\frac{27}{2}-\frac{27}{3}\] \[=\frac{27}{6}=\frac{9}{2}=4.5\,sq\,unit\]