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Question
Find the area of the region bounded by the following curves, the X-axis and the given lines: 2y + x = 8, x = 2, x = 4
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Solution
Let A be the required area.
Consider the equation 2y + x = 8
i.e., y = `(8 - x)/(2)`
∴ A = `int_2^4 y*dx`
= `int_2^4 (8 - x)/(2)*dx`
= `(1)/(2) int_2^4 (8 - x)*dx`
= `(1)/(2)[8x - x^2/2]_2^4`
= `(1)/(2)[(8 xx 4 - 4^2/2) - (8 xx 2 - 2^2/2)]`
= `(1)/(2)(32 - 8) - (16 - 2)]`
= `(1)/(2)(24 - 14)`
= `(1)/(2) xx 10`
∴ A = 5 sq. units.
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