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Question
Find the area of the region enclosed by the curves y2 = x, x = `1/4`, y = 0 and x = 1, using integration.
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Solution
The area of the region bounded by the curve, y2 = x, the line x = `1/4` and x = 4 and y = 0 (i.e., x-axis) is the a ABEF
Thus, area of ABEF = 2 area of ABCD
= `2int_(1/4)^1 ydx`
= `2int_(1/4)^1 sqrt(x)dx`
= `2[x^(3/2)/(3/2)]_(1/4)^1`
= `4/3[(1)^(3/2) - (1/4)^(3/2)]`
= `4/3[1 - 1/8]`
= `4/3[7/8]`
= `7/6` units
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