Find the area of the region bounded by the curve y = 2x+3, the X axis and the lines x = 0 and x = 2 - Mathematics and Statistics

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Sum

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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Chapter 1.7: Application of Definite Integration - Q.2

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