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Solve the following : ∫24xx2+1⋅dx - Mathematics and Statistics

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Sum

Solve the following : `int_2^4 x/(x^2 + 1)*dx`

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Solution

Let I = `int_2^4 x/(x^2 + 1)*dx`

Put x2 + 1 = t
∴ 2x·dx = dt
∴ x·dx = `"dt"/(2)`
When x = 2, t = 22 + 1 = 5
When x = 4, t = 42 + 1 = 17

∴ I = `int_5^17 (1)/"t"*"dt"/2`

= `(1)/(2) int_5^17 "dt"/"t"`

= `(1)/(2)[log|"t"|]_5^17`

= `(1)/(2)(log 17 - log 5)`

∴ I = `(1)/(2)log (17/5)`.

Concept: Fundamental Theorem of Integral Calculus
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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 4.16 | Page 150
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