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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
Solution
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
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