The area of the region bounded by `x^(2)=4y,y=1,y=4 and` the Y-axis lying in the first quadrant is . . . . . . Square units.

Options

A. `(22)/(3)`
B. `(28)/(3)`
C. `30`
D. `(27)/(4)`

Answer

B

Explanation

We have,
`x^(2)=4y`
`y=1 `
`y=4`

and the Y-axis lying in the first quadrant.
`therefore` Required area=`int_(1)^(4)sqrt(4y)dy=2[(2)/(3)y^((3)/(2))]_(1)^(4)=(4)/(3)[4^((3)/(2))-1]`
`=(4)/(3)(8-1)=(4)/(3)xx7=(28)/(3)`