Question

Find the area of the region bounded by x2=4y,y=2,y=4 and the x-axis in the first quadrant.

Answer 1

The area of the region bounded by the curve, x2 = 4y,y=2,and y=4,and the y-axis

is the area ABCD.

Area of ABCD=$\int^4_2xdy$

=$\int^4_2 2\sqrt ydy$

=$2\int^4_2 \sqrt ydy$

=$2\bigg[\frac{y^{\frac{3}{2}}}{\frac{3}{2}}\bigg]^4_2$

=$\frac{4}{3}\bigg[(4)^{\frac{3}{2}}-(2)^{\frac{3}{2}}\bigg]$

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

=$\bigg(\frac{32-8\sqrt 2}{3}\bigg)$units