question_answer

The area between the parabola \[y={{x}^{2}}\] and the line \[y=x\] is                                                     [UPSEAT 2004]

A)            \[\frac{1}{6}\]sq. unit       

B)            \[\frac{1}{3}\]sq. unit

C)            \[\frac{1}{2}\]sq. unit       

D)            None of these

Correct Answer: A

Solution :

           Given curves are \[y={{x}^{2}}\]and \[y=x\]                    On solving, we get \[x=0\], \[x=1\]            Therefore, required area \[A=\int_{0}^{1}{({{x}^{2}}-x)}dx\]            \[=\left[ \frac{{{x}^{3}}}{3}-\frac{{{x}^{2}}}{2} \right]_{0}^{1}\]\[=\frac{1}{3}-\frac{1}{2}=\frac{1}{6}\] sq. unit.