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प्रश्न
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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उत्तर
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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