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Question
Find the area of the region bounded by the curve 4y = 7x + 9, the X-axis and the lines x = 2 and x = 8
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Solution
Let A be the required area.
Given equation of the curve is 4y = 7x + 9
i.e., y = `(7x + 9)/4`
∴ A = `int_2^8 y "d"x`
= `int_2^8 (7x + 9)/4 "d"x`
= `1/4 int_2^8 (7x + 9) "d"x`
= `1/4[7(x^2/2) + 9x]_2^8`
= `1/4[[7(8^2/2) + 9(8) - 7(2^2/2) + 9(2)]]`
= `1/4[224 + 72 - (14 + 18)]`
= `1/4(296 - 32)`
= `1/4(264)`
∴ A = 66 sq.units
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