Find the area of the region bounded by the curve ` x^(2) = 16 y `, lines ` y = 2, y = 6 ` and Y - axis lying in the first quadrant.

Explanation

Given curve is `x^(2) = 16y`
Required area ` = int_(2)^(6) x.dy`
` therefore " "A = int_(2)^(6)sqrt(16y)dy`

` = 4. [(2)/(3)y^(3//2)]_(2)^(6)`
` = (8)/(3)(6sqrt(6) - 2sqrt(2))`
` = (16)/(3)(3sqrt(6)- sqrt(2))`sq unit.
= 31.65 sq units.