# Fill in the blank : ∫23xx2-1⋅dx = _______ - Mathematics and Statistics

Fill in the Blanks

Fill in the blank : int_2^3 x/(x^2 - 1)*dx = _______

#### Solution

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).

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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 6 Definite Integration
Miscellaneous Exercise 6 | Q 2.06 | Page 149
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