Question

Find the area of the region bounded by y² = 25x and the line x = 4.

Answer 1

Required area = area of the region OABO = 2(area of the region OACO)

= `2 int_0^4 y  dx`, where y² = 25x, i.e. y = 5`sqrt x`

= `2 int_0^4 5 sqrt x dx`

= `10 int_0^4 x^(1/2) dx`

= `10[(x^(3/2))/((3/2))]_0^4`

= `20/3[x^(3/2)]_0^4`

= `20/3 [8 - 0]`

= `160/3` sq. units.