Question

The area of the region lying between the line x-y+2=0 and the curve x= $\sqrt { y }$ is

• A. 9
• B. $\frac { 9 } { 2 }$
• C. $\frac { 10 } { 3 }$
• D. None of these

Answer 1

Answer: (C)

$\frac { 10 } { 3 }$

Answer 2

Required Area

$= \int _ { 0 } ^ { 2 } \left[ ( x + 2 ) - \left( x ^ { 2 } \right) d x = \left[ \frac { x ^ { 2 } } { 2 } + 2 x - \frac { x ^ { 3 } } { 3 } \right] _ { 0 } ^ { 2 } \right]$ $= 2 + 4 - \frac { 8 } { 3 } = \frac { 10 } { 3 }$