Question

Find the area of the region bounded by the parabola y² = 16x and the line x = 4

Answer 1

Given equation of the curve is y² = 16x

y² =

∴ y = `+-  4sqrt(x)`

∴ y = `4 sqrt(x)`    ......[∵ In first quadrant, y > 0]

Required area = Area of the region OBSAO

= 2   .......(Area of the region OSAO)

= `2int_0^4 y  "d"x`

= `2 int_0^4 4sqrt(x)  "d"x`

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

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

= `16/3(8)`

= `128/3` sq.units