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प्रश्न
Find the area of the region bounded by the following curves, X-axis and the given lines: y2 = 16x, x = 0, x = 4
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उत्तर
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 4 sqrt(x)*dx`
= `8[(x^(3/2))/(3/2)]_0^4`
= `16/3[x^(3/2)]_0^4`
= `16/3[(4)^(3/2) - (0)^(3/2)]`
= `16/3 (8)`
A = `(128)/(3) "sq. units"`.
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