Question

Find the area of the region bounded by the curve y² = 8x, the X−axis and the given lines x = 1, x = 3, y ≥ 0

Answer 1

Let A be the required area.

Consider the equation y² = 8x.

∴ A = `int_1^3 y  "d"x`

= `int_1^3 sqrt(8x)  "d"x`

= `2sqrt(2)[(x^(3/2))/(3/2)]_1^3`

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

= `(4sqrt(2))/3 (3sqrt(3) - 1)` sq.units