Question

Fill in the blank :

Area of the region bounded by x² = 16y, y = 1, y = 4 and the Y-axis, lying in the first quadrant is _______.

Answer 1

Required area = `int_1^4x*dy`

= `int_1^4 4sqrt(y)*dy`

= `4[y^(3/2)/(3/2)]_1^4`

= `(8)/(3)[(4)^(3/2) - (1)^(3/2)]`

= `(8)/(3)(8 - 1)`

= `(56)/(3)"sq.units"`.