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Find the area of the region bounded by the following curves, X-axis and the given lines : xy = 2, x = 1, x = 4 - Mathematics and Statistics

Sum

Find the area of the region bounded by the following curves, X-axis and the given lines: xy = 2, x = 1, x = 4

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Solution

For xy = 2, y = `(2)/x`.

Required area = `int_1^4 y*dx,  "where"  y = (2)/x`

= `int_1^4 (2)/x*dx`

= `[2 log |x|]_1^4`

= 2 log 4 – 2 log 1
= 2 log 4 – 0
= 2 log 4 sq units.

Concept: Area Bounded by the Curve, Axis and Line
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 5 Application of Definite Integration
Exercise 5.1 | Q 1.5 | Page 187
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