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Question
Find the area of the region bounded by the following curves, X-axis and the given lines : y2 = x, x = 0, x = 4
Solution
The required area consists of two bounded regions A1 and A2 which are equal in areas.
For y2 = x, y = `sqrt(x)`
Required area = A1 + A2 = 2A1
= `2int_0^4 y*dx, "where" y = sqrt(x)`
= `2int_0^4 sqrt(x)*dx`
= `2[(x^(3/2))/(3/2)]_0^4`
= `2[2/3(4)^(3/2) - 0]`
= `2[2/3(2^2)^(3/2)]`
= `(32)/(3) "sq units"`.
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