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Question
Find the area of the region bounded by the curve y = `sqrt(2x + 3)`, the X axis and the lines x = 0 and x = 2
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Solution
Let A be the required area.
Given equation of the curve is y = `sqrt(2x + 3)`
∴ A = `int_0^2 y "d"x`
= `int_0^2 sqrt(2x + 3) "d"x`
= `int_0^2 (2x + 3)^(1/2) "d"x`
= `[((2x + 3)^(3/2))/(3/2) xx 1/2]_0^2`
= `1/3[(2x + 3)^(3/2)]_0^2`
= `1/3[(4 + 3)^(5/2) - (0 + 3)^(3/2)]`
= `1/3[(7)^(3/2) - (3)^(3/2)]`
∴ A = `1/3(7sqrt(7) - 3sqrt(3))` sq.units
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