Question

The area of the region bounded by the curve y² = 4x and x = 1 is ______.

विकल्प

• `4/3`

• `8/3`

• `64/3`

• `32/3`

Answer 1

The area of the region bounded by the curve y² = 4x and x = 1 is `underlinebb(8/3)`.

Explanation:

Required area OABC = `2 xx int_0^1 y  dx`

= `2 xx int_0^1 2sqrtx  dx`

= `4 xx int_0^1 x^(1/2) dx = 4 xx [(x^(1/2 +1))/(1/2 + 1)]_0^1`

= `4  .(x^(3/2)/(3/2))_0^1 = 8/3 (x^(3/2))_0^1` 

= `8/3 xx 1`

= `8/3` sq units