Question

Choose the correct alternative :

`int_2^3 x/(x^2 - 1)*dx` =

विकल्प

• `log (8/3)`

• `-log (8/3)`

• `(1)/(2)log(8/3)`

• `(-1)/(2)log(8/3)`

Answer 1

Let I = `int_2^3 x/(x^2 - 1)*dx`
Put x² – 1 = t
∴ 2x·dx = dt

∴ x·dx = `(1)/(2)*dt`

When x = 2, t = 2² – 1 = 3
When x = 3, t = 3² – 1 = 8

∴ I = `int_3^8 (1)/"t"*"dt"/(2)`

= `(1)/(2)int_3^8 "dt"/"t"`

= `(1)/(2)[log |"t"|]_3^8`

= `(1)/(2)(log 8 - log 3)`

∴ I = `(1)/(2) log (8/3)`.