Question

Area bounded by parabola $y ^ { 2 } = x$ and straight line $2 y = x$ is

• A. $\frac { 4 } { 3 }$
• B. 1
• C. $\frac { 2 } { 3 }$
• D. $\frac { 1 } { 3 }$

Answer 1

Answer: (A)

$\frac { 4 } { 3 }$

Answer 2

$y ^ { 2 } = x$ and $2 y = x \Rightarrow y ^ { 2 } = 2 y \Rightarrow y = 0,2$

Required area

$= \int _ { 0 } ^ { 2 } \left( y ^ { 2 } - 2 y \right) d y = \left( \frac { y ^ { 3 } } { 3 } - y ^ { 2 } \right) _ { 0 } ^ { 2 } = \frac { 4 } { 3 }$ sq. unit.