Question

The area of the region bounded by parabola y² = x and the straight line 2y = x is ______.

Options

• `4/3`sq.units

• 1 sq.units

• `2/3`sq.units

• `1/3`sq.units

Answer 1

The area of the region bounded by parabola y² = x and the straight line 2y = x is `4/3`sq.units.

Explanation:

Given equation of parabola is y² = x   ......(i)

And equation of straight line is 2y = x  ......(ii)

Solving equation (i) and (ii)

We get `(x/2)^2` = x

⇒ `x^2/4` = x

⇒ x² = 4x

⇒ x(x – 4) = 0

∴ x = 0, 4

Required area = `int_0^4 sqrt(x)  "d"x - int_0^4  x/2  "d"x`

= `2/3 [x^(3/2)]_0^4 - 1/2 * 1/2 [x^2]_0^4`

= `2/3 [(4)^(3/2) - 0] - 1/4 [(4)^2 - 0]`

= `2/3 xx 8 - 1/4 xx 16`

= `16/3 - 4`

= `4/3` sq.units