Question

Find the area of the region bounded by the curve y² = 4x, the X-axis and the lines x = 1, x = 4 for y ≥ 0.

Answer 1

Let A be the required area.

A = `int_1^4 y  dx`

= `int_1^4 2sqrt(x)  dx`

= `2 int_1^4 x^(1/2)  dx`

= `2  . 2/3 [x^(3/2)]_1^4`

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

A = `28/3` sq. units.