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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Find the area of the region bounded by the curve 4y = 7x + 9, the X-axis and the lines x = 2 and x = 8 - Mathematics and Statistics

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प्रश्न

Find the area of the region bounded by the curve 4y = 7x + 9, the X-axis and the lines x = 2 and x = 8

बेरीज
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उत्तर

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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पाठ 1.7: Application of Definite Integration - Q.2

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