Question

Find the area of region bounded by the line x = 2 and the parabola y² = 8x

Answer 1

Here, y² = 8x and x = 2

y² = 8(2) = 16

∴ y = ±4

Required area = `2 int_0^2 sqrt(8x)  "d"x`

= `2 xx 2sqrt(2) int_0^2 sqrt(x)  "d"x`

= `4sqrt(2) xx 2/3 [x^(3/2)]_0^2`

= `(8sqrt(2))/3 [(2)^(3/2)]`

= `(8sqrt(2))/3 xx 2sqrt(2)`

= `32/3` sq.units

Hence, the area of the region = `32/3` sq.units