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**Solve the following :**

Find the area of the region bounded by the straight line 2y = 5x + 7, X-axis and x = 2, x = 5.

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#### Solution

The equation of the line is 2y = 5x + 7,

i.e. y = `(5)/(2)x + (7)/(2)`

Required area = area of the region ABCDA

= area under the line y = `(5)/(2)x + (7)/(2)` between x = 2 and x = 5

= `int_2^5 (5/2x + 7/2)*dx`

= `(5)/(2)* int_2^5x*dx + (7)/(2) int_2^5 1*dx`

= `(5)/(2)[x^2/2]_2^5 + (7)/(2)[x]_2^5`

= `(5)/(2)[25/2 - 4/2] + (7)/(2)[5 - 2]`

= `(5)/(2) xx (21)/(2) + (21)/(2)`

= `(105)/(4) + (42)/(4)`

= `(147)/(4)"sq units"`.

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