Question

Find the area of the region bounded by the curve (parabola) y² = 4x and the line

Answer 1

Curve is y² = 4x and line is x = 3

Required area= Area POCP Area QOCP

= 2 (Area POCP)

= 2 `int_0^3 y  dx `

= 2 `int_0^3  sqrt4x  dx `

= 4 `int_0^3  x^(1/2)  dx `

= 4 `[(x3/2)/(3/2)]_0^3`

= 4. `2/3 [x^(3/2) - o^(3/2)]`

= `8/3  3sqrt3`

Requires area = 8`sqrt3` sq. units.