Question

The area of the region bounded by the curve $y = x - x ^ { 2 }$between x = 0and x = 1is

• A. $\frac { 1 } { 6 }$
• B. $\frac { 1 } { 3 }$
• C. $\frac { 1 } { 2 }$
• D. $\frac { 5 } { 6 }$

Answer 1

Answer: (A)

$\frac { 1 } { 6 }$

Answer 2

Required Area $= \int _ { 0 } ^ { 1 } \left( x - x ^ { 2 } \right) d x = \left[ \frac { x ^ { 2 } } { 2 } - \frac { x ^ { 3 } } { 3 } \right] _ { 0 } ^ { 1 }$ $= \frac { 1 } { 2 } - \frac { 1 } { 3 } = \frac { 1 } { 6 }$.