Maharashtra State BoardHSC Commerce 12th Board Exam
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Solve the following : Find the area of the region bounded by the curve xy = c2, the X-axis, and the lines x = c, x = 2c. - Mathematics and Statistics

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Sum

Solve the following :

Find the area of the region bounded by the curve xy = c2, the X-axis, and the lines x = c, x = 2c.

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Solution

Given equation of the curve is xy = c2

∴ y = `"c"^2/x`

∴ Required area = `int_"c"^(2"c") y*dx`

= `int_"c"^(2"c") "c"^2/x*dx`

= `"c"^2 int_"c"^(2c") (1/x)*dx`

= `"c"^2 [logx]_"c"^(2"c")`

= c2(log 2c – log c)

= `"c"^2 log ((2"c")/"c")`

= c2 log 2 sq.units.

Concept: Area Under Simple Curves
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 7 Applications of Definite Integration
Miscellaneous Exercise 7 | Q 4.1 | Page 158
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