Question

Calcualte the area under the curve y = `2sqrt(x)` included between the lines x = 0 and x = 1

Answer 1

Given the curves y = `2sqrt(x)`, x = 0 and x = 1.

y = `2sqrt(x)`

⇒ y² = 4x   ......(Parabola)

Required area = `int_0^1 (2sqrt(x))  "d"x`

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

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

= `4/3` sq.units

Hence, required area = `4/3` sq.units