Question

Find the area of the region bounded by the curve x² = 12y, the Y−axis and the given lines y = 2, y = 4, x ≥ 0

Answer 1

Let A be the required area.

Consider the equation x² = 12y

∴ A = `int_2^4 x  "d"y`

= `int_2^4 sqrt(12y)  "d"y`

= `2sqrt(3) [(y^(3/2))/(3/2)]_2^4`

= `(4sqrt(3))/3 [(4)^(3/2) - (2)^(3/2)]`

= `4/sqrt(3) (8 - 2sqrt(2))`

= `8/sqrt(3) (4 - sqrt(2))` sq.units