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Question
Find the area of the region bounded by the curve x2 = 16y, lines y = 2, y = 6 and Y-axis lying in the first quadrant.
Solution
y varies from y = 2 to y = 6.
Equation of parabola x2 = 16y
`x=4sqrty`
Required area = `int_a^bxdy`
`=int_2^64sqrtydy`
`=4[y^(1/2)/(3/2)]_2^6`
`=4xx2/3[(6)^(3/2)-2^(3/2)]`
`=8/3[6^(3/2)-2^(3/2)]`sq. units
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