Question

Find the area bounded between the curve $y ^ { 2 } = 2 y - x$ and

y-axis .

• A. $\frac { 4 } { 3 }$
• B. $\frac { 2 } { 3 }$
• C. $\frac { 1 } { 3 }$
• D. $5$

Answer 1

Answer: (A)

$\frac { 4 } { 3 }$

Answer 2

The area between the given curve $x = 2 y - y ^ { 2 }$ and y- axis will be as shown in diagram

∴ Required Area$= \int _ { 0 } ^ { 2 } \left( 2 y - y ^ { 2 } \right) d y$

$= \left[ y ^ { 2 } - \frac { y ^ { 3 } } { 3 } \right] _ { 0 } ^ { 2 } = \frac { 4 } { 3 }$