What is the area of the region bounded by the curve y=square root(x-1), y axis and y=1 to y=5 ?
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
The required area is 136/3
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