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

Explanation

Equation of parabola `x^(2)=4y.`
Area of region bounded by `x^(2)=4y,y=2,y=4` and Y-axis
`=` Area of ABCDA
`=int_(2)^(4)"x "dy==int_(2)^(4)2sqrt(y)" "dy`
`=2.[(y^(3//2))/(3//2)]_(2)^(4)=(4)/(3 )[4^(3//2)-2^(3//2)]`
`=(4)/(3)(8-2sqrt(2))sq.` units
`=(8)/(3)(4-sqrt(2))sq.` units