Question

Find the area of the region bounded by the parabola x² = 4y and The X-axis and the line x = 1, x = 4

Answer 1

Given equation of the parabola is x² = 4y.

Required area = `int_1^4 y  "d"x`

= `int_1^4 x^2/4  "d"x`

= `1/4[x^3/3]_1^4`

= `1/12(4^3 - 1^3)`

= `1/12(64 - 1)`

= `63/12`

= `21/4` sq.units