Question

Find the area of the region bounded by $x^2=4y$, the y-axis and the abscissae y=2 and y=4, in the first quadrant.

Answer 1

$x^2=4y$

$y=2,y=4$

$x=2\sqrt{y}$

$\Delta ={\int }_2^{4}xdy$

$={\int }_2^{4}2\sqrt{4}dy$

${[\frac{2.2}{3}.y^{3/2}]}_2^4$

$=\frac{4}{3}[2^{-2\times \frac{3}{2}}-2^{\frac{3}{2}}]$

$=\frac{4}{3}[8-2\sqrt{2}]=\frac{32-8\sqrt{2}}{3}$