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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.
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Solution
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
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