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प्रश्न
Using Integration, find the area of the region bounded the line 2y + x = 8, the x-axis and the lines x = 2, x = 4
उत्तर
The equation of the line given is 2y + x = 8
⇒ 2y = 8 – x
⇒ y = `(8 - x)/2`
y = `4 - x/2`
Also x varies from 2 to 4
Required Area
A = `int_"a"^"b" y "d"x`
= `int_2^4 (4 - x/2) "d"x`
= `[4x - 1/2 (x^2/2)]_2^4`
= `[4x - x^2/4]_2^4`
= `[4(4) - (4)^2/4] - [4(2) - (2)^2/4]`
= `[16 - 16/4] - [8 - 4/4]`
= (16 – 4) – (8 – 1)
= 12 – 7
= 5 sq.units
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