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

Sum

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

#### 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
Is there an error in this question or solution?

#### 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