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.

Answer 1

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