# Q : 3       Find the area of the region bounded by  $\dpi{100} x^2=4y,y=2,y=4$  and the $\dpi{100} y$-axis in the first quadrant.

D Divya Prakash Singh

The area bounded by the curves  $\dpi{100} x^2=4y,y=2,y=4$  and the $\dpi{100} y$-axis in the first  quadrant is ABCD.

$= \int^4_{2} x dy$

$= \int^4_{2} 2\sqrt{y} dy$

$= 2\int^4_{2} \sqrt{y} dy$

$=2\left \{ \frac{y^{\frac{3}{2}}}{\frac{3}{2}} \right \}^4_{2}$

$= \frac{4}{3}\left \{ (4)^{\frac{3}{2}}-(2)^{\frac{3}{2}} \right \}$

$= \frac{4}{3} \left \{ 8 -2\sqrt 2 \right \}$

$= \left \{ \frac{32-8\sqrt 2}{3} \right \}\ units.$

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