Question

Find the area of the region bounded by the following curves, X-axis and the given lines: y² = 16x, x = 0, x = 4

Answer 1

The required area consists of two bounded regions A₁ and A₂ which are equal in areas.

For y² = x, y = `sqrt(x)`

Required area = A₁ + A₂ = 2A₁

= `2int_0^4 y*dx,  "where"  y = sqrt(x)`

= `2int_0^4 4 sqrt(x)*dx`

= `8[(x^(3/2))/(3/2)]_0^4`

= `16/3[x^(3/2)]_0^4`

= `16/3[(4)^(3/2) - (0)^(3/2)]`

= `16/3 (8)`

A = `(128)/(3) "sq. units"`.