Question

The area between the parabola $y = x ^ { 2 }$ and the line $y = x$ is

• A. $\frac { 1 } { 6 }$sq. unit
• B. $\frac { 1 } { 3 }$sq. unit
• C. $\frac { 1 } { 2 }$ sq. unit
• D. None of these

Answer 1

Answer: (A)

$\frac { 1 } { 6 }$sq. unit

Answer 2

Given curves are $y = x ^ { 2 }$ and $y = x$

On solving, we get$x = 0$, $x = 1$

Therefore, required area

$A = \int _ { 0 } ^ { 1 } \left( x ^ { 2 } - x \right) d x$

$= \left[ \frac { x ^ { 3 } } { 3 } - \frac { x ^ { 2 } } { 2 } \right] _ { 0 } ^ { 1 }$ $= \frac { 1 } { 3 } - \frac { 1 } { 2 } = \frac { 1 } { 6 }$ sq. unit.