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Question
Find the area of the region bounded by the following curves, the X-axis and the given lines: 2y = 5x + 7, x = 2, x = 8
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Solution
Let A be the required area.
Consider the equation 2y = 5x + 7
i.e. y = `(5x + 7)/(2)`
∴ A = `int_2^8 y*dx`
= `int_2^8 (5x + 7)/(2)*dx`
= `(1)/(2) int_2^8 (5x + 7)*dx`
= `(1)/(2)[(5x^2)/(2) + 7x]_2^8`
= `(1)/(2)[((5 xx 8^2)/2 + 7 xx 8) - ((5 xx 2^2)/2 + 7 xx 2)]`
= `(1)/(2)[(160 + 56) - (10 + 14)]`
= `(1)/(2)(216 - 24)`
= `(1)/(2) xx 192`
∴ A = 96 sq. units.
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