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Question
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.
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