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.
`:.` Required area `= int_(1)^(4) sqrt(4 y) dy`
`=2[(2)/(3) y^(3/2)]_(1)^(4)= (4)/(3) [4^(3/2) -1]`
`=(4)/(3) (8-1) = (4)/(3) xx 7 = (28)/(3)`