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Question
Using integration, find the area of the region bounded by the line 2y + x = 8 , X−axis and the lines x = 2 and x = 4
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Solution
Let A be the required area.
Consider the equation 2y + x = 8.
∴ y = `1/2(8 - x)`
∴ Required area = `int_2^4 y "d"x`
= `int_2^4 1/2(8 - x) "d"x`
= `1/2[8x - x^2/2]_2^4`
= `1/2[(8(4) - 4^2/2) - (8(2) - ^2/2)]`
= `1/2[(32 - 8) - (16 - 2)]`
= 5 sq.units
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