What is the area of the region bounded by the curve y=square root(x-1), y axis and y=1 to y=5 ?

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The area of the region bounded by the curve y = sqrt (x - 1), the y- axis and the lines y = 1 and y = 5 is the limited integral of the expression of x in terms of y, between y = 5 and y = 1.

y = sqrt (x - 1)

=> y^2 = x - 1

=> x = y^2 + 1

Int [ x dy] = Int [ y^2 + 1 dy]

=> y^3 / 3 + y + C

Between y = 1 and y = 5,

=> 5^3 / 3 + 5 + C - 1^3/3 - 1 - C

=> 124/3 + 4

=> 136/3

The required area is 136/3

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