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Question
Find the area of the region bounded by the lines 2y + x = 8, x = 2 and x = 4.
Solution
Given area are 2y + x = 8, x = 2 and x = 4
Required area = `int_2^4 y dx`
= `int_2^4 ([ 8 - x ]/2) dx`
= `int_2^4 (4 -1/2x)dx`
= `[ 4x - 1/2 x^2/2]_2^4`
= `[ 4 xx 4 - 1/4 (4)^2] - [ 4 xx 2 - 1/4 (2)^2 ]`
= 12 - 7 = 5
∴ Required area = 5 sq. units
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