Question

Using integration, find the area of the region bounded between the line x = 4 and the parabola y² = 16x.

Answer 1

The shaded region OACO is the region bounded by the parabola y² = 16x and the line x = 4.

The area OACO is symmetrical about X-axis.

Area of OACO = 2(Area of OAB)

= `2 int_0^4 "y dx"`

= `2 int_0^4 4sqrt"x"  "dx"`

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

= `16/3 (4)^(3//2)`

= `16/3 xx 8`

= `128/3`

So, the required area is `128/3` sq. units.