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.

Answer 1

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.