Maharashtra State BoardHSC Commerce 12th Board Exam
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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` = _______

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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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