# Fill in the blank : ∫01dx2x+5 = _______ - Mathematics and Statistics

Fill in the Blanks

Fill in the blank : int_0^1 dx/(2x + 5) = _______

#### Solution

Let I = int_0^1 dx/(2x + 5)

Put 2x + 5 = t
∴ 2dx = dt
∴ dx = "dt"/(2)
When x = 0, t = 2(0) + 5 = 5
When x = 1, t = 2(1) + 5 = 7

∴ I = (1)/(2) int_5^7 "dt"/"t"

= (1)/(2)[log|"t"|]_5^7

= (1)/(2)(log 7 - log 5)

= (1)/(2)log(7/5).

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 2.03 | Page 149