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Find area of the region bounded by 2x + 4y = 10, y = 2 and y = 4 and the Y-axis lying in the first quadrant

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#### Solution

Let A be the required area.

Given equation of curve 2x + 4y = 10

i.e., x = 5 – 2y

∴ A = `int_2^(5/2) x "d"y`

= `int_2^(5/2) (5 - 2) "d"y`

= `[5y - (2y^2)/2]_2^(5/2)`

= `[5y - y^2]_2^(5/2)`

= `[5(5/2) - (5/2)^2] - [5(2) - (2)^2]`

= `25/2 - 25/4 - (10 - 5)`

= `25/2 - 6`

= `1/4` sq.units

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