Question

Draw a rough sketch of the curve y = `sqrt(x - 1)` in the interval [1, 5]. Find the area under the curve and between the lines x = 1 and x = 5.

Answer 1

Here, we have y = `sqrt(x - 1)`

⇒ y² = x – 1   ......(Parabola)

Area of the required region

= `int_1^5 sqrt(x - 1)  "d"x`

= `2/3 [(x - 1)^(3/2)]_1^5`

= `2/3 [(5 - 1)^(3/2) - 0]`

= `2/3 xx (4)^(2/3)`

= `2/3 xx 8`

= `16/3` sq.units