#### Question

Find the area of the region bounded by the curve x^{2} = 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 x^{2} = 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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#### APPEARS IN

Solution Find the area of the region bounded by the curve x^2 = 16y, lines y = 2, y = 6 and Y-axis lying in the first quadrant. Concept: Area of the Region Bounded by a Curve and a Line.