Question

Find the area of the region bounded by the curves y² = 9x, y = 3x

Answer 1

We have, y² = 9x, y = 3x

Solving the two equations,

We have (3x)² = 9x

⇒ 9x² – 9x = 0

⇒ 9x(x – 1) = 0

∴ x = 0, 1

Area of the shaded region

= ar (region OAB) – ar (ΔOAB)

= `- int_0^1 y_1 * "d"x`

= `int_0^1 sqrt(9x)  "d"x - int_0^1 3x  "d"x`

= `3 int_0^1 sqrt(x)  "d"x - 3 int_0^1 x  "d"x`

= `3 xx 2/3 [x^(3/2)]_0^1 - 3[x^2/2]_0^1`

= `2[(1)^(3/2) - 0] - 3/2 [(1)^2 - 0]`

= `2(1) - 3/2 (1)`

= `2 - 3/2`

= `1/2` sq.units

Hence, the required area = `1/2` sq.units