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Question
Find area of the region bounded by the parabola x2 = 4y, the Y-axis lying in the first quadrant and the lines y = 3
Solution
Given equation of the parabola is x2 = 4y
∴ x = `2sqrt(y)` ......[∵ In first quadrant x > 0]
∴ Required area = `int_0^3 2sqrt(y) "d"y`
= `2 int_0^3 sqrt(y) "d"y`
= `3[(y^(3/2))/(3/2)]_0^3`
= `4/3[(3)^(3/2) - 0]`
= `4/3(3sqrt(3))`
= `4sqrt(3)` sq.units
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